## Solutions for Physics for Scientists and Engineers: Foundations and Connections

# Browse All Chapters of This Textbook

Chapter 1 - Getting StartedChapter 1.5 - System Of UnitsChapter 1.6 - Dimensional AnalysisChapter 1.7 - Error And Significant FiguresChapter 2 - One Dimensional MotionChapter 2.2 - Motion DiagramsChapter 2.3 - Coordinate Systems And PositionChapter 2.5 - Displacement And Distance TraveledChapter 2.6 - Average Velocity And SpeedChapter 2.8 - Average And Instantaneous Acceleration

Chapter 3 - VectorsChapter 3.1 - Geometric Treatment Of VectorsChapter 3.2 - Cartesian Coordinate SystemsChapter 3.3 - Components Of A VectorChapter 4 - Two-and-three Dimensional MotionChapter 4.1 - What Is Multidimensional MotionChapter 4.2 - Motion Diagrams For Multidimensional MotionChapter 4.3 - Position And DisplacementChapter 4.5 - Special Case Of Projectile MotionChapter 4.6 - Special Case Of Uniform Circular MotionChapter 4.8 - Relative Motion In Two DimensionChapter 5 - Newton's Laws Of MotionChapter 5.2 - Newton's First LawChapter 5.3 - ForceChapter 5.4 - Inertial MassChapter 5.5 - Inertial Reference FramesChapter 5.6 - Newton's Second LawChapter 5.7 - Some Specific ForcesChapter 5.9 - Newton's Thirds LawChapter 6 - Applications Of Newton’s Laws Of MotionChapter 6.1 - Newton’s Laws In A Messy WorldChapter 6.3 - A Model For Static FrictionChapter 6.4 - Kinetic And Rolling FrictionChapter 6.5 - Drag And Terminal SpeedChapter 6.6 - Centripetal ForceChapter 7 - GravityChapter 7.1 - A Knowable UniverseChapter 7.2 - Kepler’s Laws Of Planetary MotionChapter 8 - Conservation Of EnergyChapter 8.1 - Another Approach To Newtonian MechanicsChapter 8.2 - EnergyChapter 8.3 - Gravitational Potential Energy Near The EarthChapter 9 - Energy In Nonisolated SystemsChapter 9.4 - Work Done By A Nonconstant ForceChapter 9.6 - Particles, Objects, And SystemsChapter 9.7 - Thermal EnergyChapter 9.9 - PowerChapter 10 - Systems Of Particles And Conservation Of MomentumChapter 10.1 - A Second Conservation PrincipleChapter 10.3 - Center Of Mass RevisitedChapter 10.5 - Conservation Of MomentumChapter 11 - CollisionsChapter 11.1 - What Is A Collision?Chapter 11.2 - ImpulseChapter 11.3 - Conservation During A CollisionChapter 11.5 - One-dimensional Elastic CollisionsChapter 11.6 - Two-dimensional CollisionsChapter 12 - Rotation I: Kinematics And DynamicsChapter 12.1 - Rotation Versus TranslationChapter 12.2 - Rotational KinematicsChapter 12.5 - TorqueChapter 13 - Rotation Ii: A Conservation ApproachChapter 13.1 - Conservation ApproachChapter 13.6 - Angular MomentumChapter 13.7 - Conservation Of Angular MomentumChapter 14 - Static Equilibrium, Elasticity, And FractureChapter 14.1 - What Is Static Equilibrium?Chapter 14.2 - Conditions For EquilibriumChapter 14.4 - Elasticity And FractureChapter 15 - FluidsChapter 15.1 - What Is A Fluid?Chapter 15.3 - PressureChapter 15.4 - Archimedes’s PrincipleChapter 16 - OscillationsChapter 16.1 - Picturing Harmonic MotionChapter 16.2 - Kinematic Equations Of Simple Harmonic MotionChapter 16.5 - Special Case: Object–spring OscillatorChapter 16.6 - Special Case: Simple PendulumChapter 17 - Traveling WavesChapter 17.2 - PulsesChapter 17.3 - Harmonic WavesChapter 17.5 - Sound: Special Case Of A Traveling Longitudinal WaveChapter 17.6 - Energy Transport In WavesChapter 18 - Superposition And Standing WavesChapter 18.1 - SuperpositionChapter 18.2 - ReflectionChapter 18.3 - InterferenceChapter 18.8 - BeatsChapter 19 - Temperature, Thermal Expansion And Gas LawsChapter 19.1 - Thermodynamics And TemperatureChapter 19.2 - Zeroth Law Of ThermodynamicsChapter 19.3 - Thermal ExpansionChapter 19.4 - Thermal StressChapter 19.5 - Gas LawsChapter 19.6 - Ideal Gas LawChapter 20 - Kinetic Theory Of GasesChapter 20.2 - Average And Root-mean-square QuantitiesChapter 20.3 - The Kinetic Theory Applied To Gas Temperature And PressureChapter 20.5 - Mean Free PathChapter 20.7 - Phase ChangesChapter 20.8 - EvaporationChapter 21 - Heat And The First Law Of ThermodynamicsChapter 21.2 - How Does Heat Fit Into The Conservation Of EnergyChapter 21.3 - The First Law Of ThermodynamicsChapter 21.4 - Heat Capacity And Specific HeatChapter 21.7 - Specific Thermodynamic ProcessesChapter 22 - Entropy And The Second Law Of ThermodynamicsChapter 22.2 - Heat EnginesChapter 22.4 - The Most Efficient EngineChapter 22.5 - Case Study: RefrigeratorsChapter 22.7 - Second Law Of Thermodynamics General StatementsChapter 22.9 - Entropy, Probability, And The Second LawChapter 23 - Electric ForcesChapter 23.2 - Models Of Electrical PhenomenaChapter 23.3 - A Qualitative Look At The Electrostatic ForceChapter 23.4 - Insulators And ConductorsChapter 24 - Electric FieldsChapter 24.2 - Special Case: Electric Field Of A Charged SphereChapter 24.3 - Electric Field LinesChapter 24.4 - Electric Field Of A Collection Of Charged ParticlesChapter 24.5 - Electric Field Of A Continuous Charge DistributionChapter 25 - Gauss’s LawChapter 25.1 - Qualitative Look At Gauss’s LawChapter 25.2 - FluxChapter 25.3 - Gauss’s LawChapter 25.4 - Special Case: Linear SymmetryChapter 25.7 - Special Case: ConductorsChapter 26 - Electric PotentialChapter 26.2 - Gravity AnalogyChapter 26.3 - Electric Potential EnergyChapter 26.4 - Electric PotentialChapter 26.5 - Special Case: Electric Potential Due To A Collection Of Charged ParticlesChapter 26.7 - Connection Between Electric Field (e) And Electric Potential (v)Chapter 26.9 - Graphing (e) And (v)Chapter 27 - Capacitors And BatteriesChapter 27.1 - The Leyden JarChapter 27.2 - CapacitorsChapter 27.3 - BatteriesChapter 27.4 - Capacitors In Parallel And SeriesChapter 27.7 - Energy Stored By A Capacitor With A DielectricChapter 28 - Current And ResistanceChapter 28.1 - Microscopic Model Of Charge FlowChapter 28.2 - CurrentChapter 28.3 - Current DensityChapter 28.5 - Resistance And ResistorsChapter 28.6 - Ohm’s LawChapter 28.7 - Power In A CircuitChapter 29 - Direct Current (dc) CircuitsChapter 29.1 - Measuring Potential Differences Between Two PointsChapter 29.2 - Kirchhoff’s Loop RuleChapter 29.4 - Kirchhoff’s Junction RuleChapter 29.5 - Resistors In ParallelChapter 30 - Magnetic Fields And ForcesChapter 30.2 - Revealing Magnetic FieldsChapter 30.3 - Ørsted’s DiscoveryChapter 30.4 - The Biot-savart LawChapter 30.8 - Magnetic Force On A Charged ParticleChapter 30.9 - Motion Of Charged Particles In A Magnetic FieldChapter 30.10 - Case Study: The Hall EffectChapter 30.12 - Force Between Two Long, Straight, Parallel WiresChapter 31 - Gauss’s Law For Magnetism And Ampère’s LawChapter 31.1 - Measuring The Magnetic FieldChapter 31.2 - Gauss’s Law For MagnetismChapter 31.3 - Ampère’s LawChapter 31.4 - Special Case: Linear SymmetryChapter 31.5 - Special Case: SolenoidsChapter 32 - Faraday’s Law Of InductionChapter 32.1 - Another Kind Of EmfChapter 32.2 - Faraday’s LawChapter 32.3 - Lenz’s LawChapter 32.4 - Lenz’s Law And Conservation Of EnergyChapter 32.5 - Case Study: Slide GeneratorChapter 32.6 - Case Study: Ac GeneratorsChapter 32.8 - Case Study: Power Transmission And TransformersChapter 33 - Inductors And Ac CircuitsChapter 33.1 - Inductors And InductanceChapter 33.2 - Back EmfChapter 33.3 - Special Case: Resistor–inductor (rl) CircuitChapter 33.4 - Energy Stored In A Magnetic FieldChapter 33.5 - Special Case: Inductor–capacitor (lc ) CircuitChapter 33.7 - Special Case: Ac Circuit With CapacitanceChapter 34 - Maxwell’s Equations And Electromagnetic WavesChapter 34.1 - Light: One Last Classical TopicChapter 34.2 - Generalized Form Of Faraday’s LawChapter 34.4 - Electromagnetic WavesChapter 34.5 - The Electromagnetic SpectrumChapter 34.6 - Energy And IntensityChapter 34.8 - PolarizationChapter 35 - Diffraction And InterferenceChapter 35.1 - Light Is A WaveChapter 35.2 - Sound Wave Interference RevisitedChapter 35.3 - Young’s Experiment: Position Of The FringesChapter 35.4 - Single-slit DiffractionChapter 35.6 - Single-slit Diffraction IntensityChapter 36 - Applications Of The Wave ModelChapter 36.2 - Circular Aperture DiffractionChapter 36.3 - Thin-film InterferenceChapter 36.4 - Diffraction GratingsChapter 36.5 - Dispersion And Resolving Power Of GratingsChapter 37 - Reflection And Images Formed By ReflectionChapter 37.2 - Law Of ReflectionChapter 37.3 - Images Formed By Plane MirrorsChapter 37.4 - Spherical MirrorsChapter 37.6 - Images Formed By Concave MirrorsChapter 38 - Refraction And Images Formed By RefractionChapter 38.1 - Law Of RefractionChapter 38.2 - Total Internal ReflectionChapter 38.3 - DispersionChapter 38.6 - Images Formed By Diverging LensesChapter 38.7 - Images Formed By Converging LensesChapter 38.9 - One-lens SystemsChapter 38.10 - Multiple-lens SystemsChapter 39 - RelativityChapter 39.1 - It’s In The Eye Of The ObserverChapter 39.2 - Special Case: Galilean RelativityChapter 39.7 - The Relativistic Doppler EffectChapter 39.10 - Newton’s Second Law And EnergyChapter 39.12 - Gravitational Lenses And Black Holes

### Book Details

Master physics with Debora Katz's new, ground-breaking calculus-based physics program, PHYSICS FOR SCIENTISTS AND ENGINEERS: FOUNDATIONS AND CONNECTIONS. Dr. Katz's one-of-a-kind case study approach enables you to connect math and physics concepts in a modern, interactive way. By leveraging physics education research (PER) best practices and her extensive classroom experience, Debora Katz addresses the areas where students like you struggle the most: linking physics to the real world, overcoming common preconceptions, and connecting the concept being taught with the mathematical steps to follow. How Dr. Katz deals with these challenges--with case studies, student dialogues, and detailed two-column examples--distinguishes this text from any other and will assist you in going "beyond the quantitative" to master your physics course.

# Sample Solutions for this Textbook

We offer sample solutions for Physics for Scientists and Engineers: Foundations and Connections homework problems. See examples below:

Chapter 1, Problem 1PQThe SI unit for length is m. Here, m is meters and 1 cm=10−2 m. Conclusion: Multiply the 0.53 cm by...Chapter 2, Problem 1PQWrite an expression for the condition. y→=(y0cos2πtT)j^ Here, y→ is the instantaneous position, y0...Chapter 2, Problem 31PQIn the problem, the particle attached to the vertical spring is pulled down and released. Sketch for...Chapter 2, Problem 46PQChapter 2, Problem 53PQChapter 2, Problem 65PQ

Chapter 2, Problem 76PQAssume that the pebble falls a distance d into the chasm in a time interval Δt1 and the sound of...Chapter 3, Problem 1PQWrite the x-component of vector A→. Ax=−4.00 units Here, Ax is the x-component of vector A→. Write...Given vector is A→=3.00i^+2.00j^+5.00k^. Write the general form of a vector (say A→) in terms of the...Write the expression to find the component form of any vector. A→=xi^+yj^+zk^ Here, x is the x...Chapter 3, Problem 42PQWrite an expression for the vector A→. A→=Axi^+Ayj^ (I) Here, A→ is the vector, Ax is the horizontal...In problem it is given that F→=3.3i^+6.3j^ and A→=1.1i^+2.1j^. Write the relation between F→ and A→....Chapter 3, Problem 74PQThe motion of an object can be one-dimensional or multi-dimension and is depending on the path of...An object is moving with a initial velocity vi→=3.00j^ m/s and with acceleration a→=2.50i^ m/s2 and...Chapter 4, Problem 14PQChapter 4, Problem 32PQChapter 4, Problem 33PQThe jetliner is travelling through the air and the air can move relative to ground. The jetliner...Chapter 4, Problem 58PQWrite the equation for velocity. ∫ifdv→=∫ifa→dt=Δv→∫ifa→dt=v→−vi (I) Here, a→ is the time in...Write the kinematic equation. yf=yi+vy0t+12at2 (I) Here, yf is the y component of final position, yi...Chapter 5, Problem 1PQChapter 5, Problem 23PQChapter 5, Problem 47PQChapter 5, Problem 50PQChapter 5, Problem 70PQChapter 5, Problem 74PQChapter 5, Problem 77PQChapter 5, Problem 79PQChapter 5, Problem 80PQChapter 6, Problem 1PQChapter 6, Problem 25PQChapter 6, Problem 27PQWrite the given expression for resistive force on the sphere. F→D=−bv→ (I) Here, F→D is the drag...Write the formula for the terminal velocity of an object. vt=2mgCρA (I) Here, vt is the terminal...The average of weight of car can be taken as two thousand pounds. Express two thousand pounds in...Assume the man as a particle of mass M and diameter equal to 0.500 m. The following figure gives the...Chapter 6, Problem 59PQChapter 6, Problem 79PQChapter 7, Problem 1PQWrite the equation for the net force on the particle. Fnet=F1−F2 (I) Here, Fnet is the net force, F1...Force on mass m1 due to mass m2 is along the x axis and is directed along the negative x direction....Write the equation for the gravitational field at a point due to a particle. g→(r)=−Gmr2r^ (I) Here,...Chapter 7, Problem 41PQWrite the expression for the gravitational force between two masses. F(r)=GMmr2 (I) Here, F(r) is...Write the equation to find the gravitational field due to Moon at a distance of Moon-Earth distance...Write the equation for the gravitational field for a mass. g→(r)=−GMr2r^ (I) Here, g→(r) is the...Chapter 8, Problem 1PQThe diagram for the position of the child is given in figure 1. Figure 1 Write the equation of...Chapter 8, Problem 32PQChapter 8, Problem 48PQChapter 8, Problem 65PQWrite the equation total energy for a satellite in a circular orbit. Etot=GmME2r Here, Etot is the...Write the expression for the conservation of energy for the situation. Ki+Ugi=Kf+Ugf (I) Here, Ki is...Chapter 8, Problem 75PQThe grapes position at different heights is shown below. Write the expression for the radius of...Chapter 9, Problem 1PQChapter 9, Problem 8PQChapter 9, Problem 10PQChapter 9, Problem 30PQIt is given that the rolling friction is negligible. This implies the principle of conservation of...Chapter 9, Problem 50PQWrite the expression for the magnitude of vector A→. A=Ax2+Ay2+Az2 (I) Here, Ax is the x component...The energy conservation equation for a system is, Ki+Ugi+Uei+Wtot=Kf+Ugf+Uef+ΔEth (I) Here, Ki is...Write the expression for the distance travelled during acceleration. Δy=v¯t (I) Here, Δy is the...Principle of conservation of energy as the name implies helps to calculate the energy by application...Chapter 10, Problem 4PQWrite the expression to find the position of the center of mass. r→CM=1M∑j=1nmjr→j Here, r→CM is the...Chapter 10, Problem 30PQWrite the equation to find the force of thrust of the rocket. F→thrust=(vE→)RdMRdt (I) Here,...Write the expression for velocity of center of mass. r→CM=∑j=1nmjrj→M=m1r1→+m2r2→m1+m2 (I) Here, m1...Chapter 10, Problem 70PQApply law of conservation of momentum to the system. The momentum of combination of sled, backpack...Consider the closed rocket exhausted fuel system and imagine an external force acting on the system....Chapter 11, Problem 1PQThe free-body diagram of the system is shown in figure 1. The two-train system only moves in x...Chapter 11, Problem 41PQChapter 11, Problem 49PQChapter 11, Problem 50PQChapter 11, Problem 51PQChapter 11, Problem 54PQChapter 11, Problem 55PQChapter 11, Problem 78PQChapter 12, Problem 1PQFrom Example 12.2, it is found that the original rotation rate is 189 rad/s. The rotation rate after...Write the equation connecting linear speed and the angular speed of a point. v=rω (I) Here, v is the...Chapter 12, Problem 35PQBoth the child in the question are situated in two different locations. But all points on a rigid...Chapter 12, Problem 53PQWrite the equation of angular speed of the wheel. dθdt=ω0e−bt (I) Here, dθ/dt is the rate of change...Given that the pin wheel rotates from θ=0° to θ=90° in a time of 0.150 s. Write the expression for...The force of static friction on the automobile must act forward and then more and more inward on the...Here the situation is pulling of a sled across a frozen lake. The system here is not completely...The hour hand and minute hand are modelled as thin rods. Write the expression for the rotational...Take R to represent the radius of both cylindrical toy as well as spherical toy, since radius will...The rotating system considered here is the Earth – Moon system. The total angular momentum of the...Assume that origin is at the Earth’s center. Write the expression for the center of mass of a...Let the radius of pottery wheel is 7 in , the approximate mass of the pottery wheel is 25.0 kg , and...Chapter 13, Problem 70PQChapter 13, Problem 73PQChapter 13, Problem 78PQChapter 14, Problem 1PQChapter 14, Problem 9PQWrite the expression for torque. τ→=r→×F→ (I) Here, τ→ is the torque on an object, r→ is the...Chapter 14, Problem 27PQChapter 14, Problem 32PQChapter 14, Problem 36PQFollowing figure gives rod and spring system. Following figure is the free body diagram of rod and...Ten forces are acting on the fan, gravity F→g acts on the center of mass. The thrust F→thrust is a...A free-body diagram is a graphical tool used to illustrate the different forces acting on a...Given that the radius of the constituent particle of alpha particle is 1.00 fm. Since nuclear...Chapter 15, Problem 17PQChapter 15, Problem 25PQChapter 15, Problem 33PQWrite the expression for density of salt water. ρsw=msalt+mwaterVtot (I) Here, ρsw is the density of...Chapter 15, Problem 40PQBernoulli’s theorem states that the energy stored in the olive oil flowing through both narrow and...Write the equation to find the distance travelled by medicine into the mouth of child. Δy=v0t+12ayt2...The volume displaced is equal to the volume of balloon. Consider volume is spherical in shape, and...Chapter 16, Problem 1PQWrite the equation to find the position of simple harmonic oscillator. y(t)=(0.850 m)cos(10.4t−5.20)...Write the expression for the velocity of the simple harmonic oscillator. vy(t)=(0.850...Write the expression for the acceleration of the simple harmonic oscillator. ay(t)=(0.850...Chapter 16, Problem 25PQChapter 16, Problem 39PQChapter 16, Problem 67PQChapter 16, Problem 74PQWrite the expression for the given solution of the equation. y(t)=Adrvcos(ωdrvt+ϕdrv) (I) Here, y(t)...Chapter 17, Problem 1PQWrite the equation for the wavelength. λ=2πk (I) Here, λ is the wavelength and k is the wave vector....Write the equation for wave function. y(x,t)=(0.0500 m)sin(3πx+π4t) (I) Here, y and x is the...Given the wave equation of the longitudinal harmonic wave. S(x,t)=(0.850)sin(10.4x−5.20t) (I) Write...Write an expression for the wave speed. v=ωk (I) Here, v is the wave speed, ω is the angular...Chapter 17, Problem 57PQIt is given that the sinusoidal wave is travelling in the negative direction. Write the general...Write the equation of intensity of sound. I=PA (I) Here, I is the intensity, P is the power and A is...The equation for the transverse wave on a string is, y(x,t)=ymaxsin(kx+ωt) (I) Here, ymax is the...Write the expression for a wave travelling along +x direction. yx(x,t)=ymaxsin(kx−ωt+φ) (I) Here,...Chapter 18, Problem 16PQWrite the expression for the natural frequencies of vibration of a wire fixed at both ends....Fundamental frequency as the name itself defines is the lowest frequency of wave generated in an...Write the equation find the wavelength of first harmonic. λ1=4Ln n=1,2,3.... Here, λ1 is the...Write the general equation for the standing wave formed when two waves travelling in opposite...Write an expression for the space between the nodes. dnodes=λ2 (I) Here, dnote is the space between...Write the expression for beat frequency fbeat=|f2−f1| (I) Here, f1 is the frequency of the tune in...Write the equation of temperature in centigrade scale. T(°C)=59[T(°F)−32] (I) Here, T(°C) is the...Write the relation between Celsius scale and Kelvin scale. T(°C)=T(K)−273.15 (I) Here, T(°C) is the...After the ball sinks, the buoyant force from the displaced liquid must be equal to the gravitational...Chapter 19, Problem 49PQChapter 19, Problem 53PQWrite the expression for the decreasing density of gasoline. ρ0=mV0 (I) Here, ρ0 is the decreasing...Chapter 19, Problem 74PQWrite the expression for volume of the wire. V=LA (I) Here, V is the volume of the wire, L is the...The atoms and molecules in gases are much more spread away from each other than in solids and...Write the equation for the average velocity in the x direction for the particles....Write the expression for average speed. vavg=∑iNviN Here, vi is the velocity and N is the number of...Write the expression for the most probable speed of gas molecules. vmp=2kBTm (I) Here, vmp is the...Write the equation of fraction of galaxy’s volume is occupied by stars. f=VstarV (I) Here, f is the...Let the ideal volume be, Videal=V0. The Van der Waals volume is 2% larger than gas volume....Given that the high temperature is 21°F, low temperature is 3°F, and the dew point is 5°F. Relative...Write the equation of ideal gas law. PV=NkBT (I) Here, P is the pressure, V is the volume, N is the...The energy transferred from a system to its surrounding or vice versa is represented by the term...Chapter 21, Problem 20PQGiven that the mas of the ice is 45.0 g, the initial temperature of the ice is −5.00°C and the final...Write the equation for the total heat transferred. Q=Q1+Q2 (I) Here, Q is the total heat energy, Q1...It is given that pressure of the gas is 2.50×105 Pa , temperature of the gas is 295 K and the gas...Given that the pressure at point A is 2.00×105 Pa, and at B is 1.00×105 Pa. The volume of as at A is...Given that the mass of the lead block is 10.0 kg, the temperature of the block is increased from...Chapter 21, Problem 80PQZan is initially existing as ice at temperature −10.00°C (263.15 K). The final state is water at 0°C...In natural world, heat flows from hotter object to colder object. But, if heat naturally flowed from...Write the expression to calculate efficiency of the diesel engine. ediesel=1−|Qc|Qh (I) Here,...Write the expression for the work done for an isobaric process. W=−P(Vf−Vi) Here, W is the work done...Write the expression for the change in entropy. ΔS=ΔQT Here, ΔS is the change in entropy, ΔQ is the...Chapter 22, Problem 71PQChapter 22, Problem 73PQWrite the expression to calculate the change in entropy of the hot reservoir. Δsh=−QhTh (I) Here,...Write the expression to calculate the entropy of reactant A. SA=∫0 K300 KcAdTT (I) Here, SA is the...The number of microstates for the combined system is the product of microstates of individual...Chapter 23, Problem 1PQChapter 23, Problem 38PQChapter 23, Problem 39PQChapter 23, Problem 40PQChapter 23, Problem 41PQChapter 23, Problem 46PQThe net-electrostatic force on the particle with charge +2.0 μC will be the sum of the force by...Chapter 23, Problem 75PQChapter 24, Problem 1PQWrite the equation for the electric field chargeq. Eq=kqr2i^ (I) Here, Eq is the electric field, q...Chapter 24, Problem 16PQChapter 24, Problem 20PQChapter 24, Problem 21PQChapter 24, Problem 51PQWrite the equation for the electric field along the axis of a charged ring. E=kQy(R2+y2)3/2 Here, E...Write the formula for the electric field created by a disk along the axis of the disk....Sketch the diagram showing the five charges. The x component of the electric field is zero based on...Chapter 25, Problem 1PQChapter 25, Problem 24PQChapter 25, Problem 32PQChapter 25, Problem 35PQChapter 25, Problem 36PQWrite the expression to find the charge enclosed. qin=∫ρdV (I) Here, ρ is the charge density and dV...Chapter 25, Problem 47PQChapter 25, Problem 67PQThe following figure marks the faces of the cube with coordinate axes. Write the expression to find...Chapter 26, Problem 1PQChapter 26, Problem 24PQThe total electric potential at origin is the sum of the potential from individual charges. Write...Chapter 26, Problem 35PQChapter 26, Problem 55PQThe electric field inside a hollow conductor is zero. Write an expression for the electric...Write an expression for the culoumb force. F=k|qQ|r2 (I) Here, k is the culoumb constant, Q is...Chapter 26, Problem 63PQWrite an expression for the total electric field equal to zero. Ey=(kqAy2+kqB(y−y')2) (I) Here, Ey...Chapter 27, Problem 1PQChapter 27, Problem 7PQWrite the formula for equivalent capacitance of capacitors in series. 1CS=1C1+1C2+1C3… Here, CS is...Chapter 27, Problem 47PQChapter 27, Problem 55PQChapter 27, Problem 75PQWrite the expression to find the equivalent capacitance of the capacitors connected in parallel....Chapter 27, Problem 85PQChapter 27, Problem 88PQThe identical metal conductor, metal 1 and metal 2 are having same number of conduction electrons...The estimated values of pure substances are given in Table 28.2. For the pure copper, the...Write the resistance of the conductor. R=ρlA (I) Here, R is resistance of the conductor, l is length...Write the relation for the electric field in the wire. Ex=−dVdx=−ΔVΔx (1) Here, Ex is electric field...Power delivered by the power supply is the same as the power radiated by the bulb. The expression...The resistivity of gold is 2.24×10−8 Ω⋅m, and that of lead is 2.065×10−7 Ω⋅m. Write the expression...Chapter 28, Problem 75PQGiven that the distance between the generating station and the switching station is 140.0 km, the...Chapter 28, Problem 82PQChapter 29, Problem 1PQRefer to Fig 29.15; in this series circuit, current is same for entire closed loop. Write the...According to Kirchhoff’s junction rule, in any junction, the sum of the all the currents entering...Chapter 29, Problem 40PQChapter 29, Problem 43PQWhen switch is open, battery ε1 does not supply voltage to the circuit. Only battery ε2 will supply...Chapter 29, Problem 45PQChapter 29, Problem 49PQChapter 29, Problem 60PQWrite the expression for the equivalent resistance for this circuit as. Req=R1R2R1+R2 (I) Here, Req...Chapter 30, Problem 1PQChapter 30, Problem 20PQRefer to figure P30.28; the direction of the magnetic field can be described by the Right hand rule....Assume that magnetic field due to smaller loop is B1 and magnetic field due to larger loop is B2....The curent flowing in all the wires is in the same direction. Therefore, the wires will be attracted...Write the expression for the approximate value of force as. B→≈μ0IR22y3j^ (I) Here, B is the...Write the expression for the magnetic field due to a current carrying wire as. B=(μ02π)Ir (I) Here,...The direction of the magnetic field at the point A is given by the Right Hand Rule. The thumb of the...Chapter 30, Problem 83PQChapter 30, Problem 91PQChapter 31, Problem 2PQDraw the figure for the system as shown below: Refer to the above figure, consider a square loop...Write the expression for Ampere’s Law for the area bounded by the curve as. ∮B.dl=μ0Ithru Rearrange...Number of turns in solenoid is the ratio of length of solenoid to the diameter of the copper wire....Write the expression for the Ampere circuital law as. ∮B⋅dl=μ0I Rearrange the above equation for I....Write the expression of the magnetic flux. ϕ=B→⋅A→ (I) Here, ϕ is the magnetic flux, B→ is the...Write the expression for the closed line integral around the Amperian loop as. ∮B⋅dl=μ0I (I) Here, B...Chapter 32, Problem 1PQChapter 32, Problem 13PQAs it is known that a three phase generator has 3 coils wound over a common armature, in away that...Faraday’s law states that, when the magnetic flux changes an emf is induced in the coil. The...Write the expression for power generated by the coil. Pavg=εrmsIrms (I) Here, Pavg is the power...Write the expression for Faraday’s law of induction. |ε|=N|d(ϕB)dt| (I) Here, ε is the induced emf,...Chapter 32, Problem 74PQWrite the expression for the induced emf. ε=−dϕBdt (I) Here, ε is the induced emf and ϕB is the...Chapter 32, Problem 79PQGiven that the two solenoids have the same number of turns per unit length, but one is short and...The following figure shows the given diagram-33.9A. Figure-(1) Here, L is inductance, R is...Chapter 33, Problem 23PQWrite the expression for average power. Pavg=∫0TdU∫0Tdt (I) Here, Pavg is the average power, U is...Write the expression to calculate the voltage across the AC generator. ε(t)=VL(t)+VR(t)+VC(t) (I)...Chapter 33, Problem 60PQChapter 33, Problem 61PQChapter 33, Problem 63PQWrite the expression for the impedance. Z=(XL2−XC2)+R2 (I) Here, XL is the inductive reactance, XC...The light has a dual nature. It sometimes behaves as particle and sometimes behaves as a wave. The...The electric and magnetic fields vary in space with time t. The electric field E(x,t) and the...Write the expression for the electric field of an electromagnetic wave. E=Emaxsin(kx−ωt)k^ (I) Here,...Write the expression for magnetic field of electromagnetic wave. B(x,t)=Bmaxsin(kx+ωt) (I) Here, k...Write the expression for the frequency of an electromagnetic wave. f=cλ (I) Here c is the speed of...Since the given equation of the electric field of the wave contains the position variable ‘z’,...Write the expression for the force of gravitation acting on the sail. Fgravity=GMmr2 (I) Here,...Write the expression for the frequency of an electromagnetic wave. f=cλ (I) Here c is the speed of...Write the expression for the amplitude of electric field. Emax=cBmax (I) Here, Emax is the amplitude...Chapter 35, Problem 1PQWrite the expression for the path difference for bright fringes in young’s double slit experiment....Write the expression for angular location of particular maximum. α=πdλsinθ (I) Here, λ is wavelength...Write the expression for the minima of single slit diffraction pattern to find sinθm....Write the expression for the path difference for bright fringes in Young’s double slit experiment....Write the expression for the speed of the wave. v=fλ (I) Here, v is the speed of the wave, λ is the...Write the for the phase difference for the wave of light 580 nm. dsinθn=nλ1 (I) Here, θn is the...Write the expression for the phase difference for the dark fringes for wavelength λ1....Write the relation of the path difference for bright fringe in young’s double slit experiment....Chapter 35, Problem 89PQChapter 36, Problem 1PQWrite the expression for the limit of resolution of the optical system. θmin=1.22λd (I) Here, λ is...Write the condition for constructive interference. w=(m+12)λ02n Here, w is the thickness of film, λ0...Write the expression for the grating spacing. d=1n (I) Here, d is the grating spacing, n is the...Write the expression for mth maxima of diffraction grating. dsinθ=mλsinθ=mλdθ=sin−1(mλd) (I) Here, d...Write the expression for mth maxima of diffraction grating. dsinθ=mλsinθ=mλdθ=sin−1(mλd) (I) Here, d...Chapter 36, Problem 62PQChapter 37, Problem 1PQChapter 37, Problem 15PQWrite the expression for magnification of the plane mirror. M=−did0 (I) Here, d0 is the object...Write the expression for magnification produced by the mirror. m=−did0=hih0 Here,m is the...Write the equation for the focal length of the mirror. f=R2 (I) Here, f is the focal length and R is...Write the equation for the mirror. 1f=1d0+1di (I) Here, f is the focal length of the mirror, d0 is...In case of convex mirror, no matter where the object is placed. The image is always erect and...Write the expression for the angle at which two tangent rays diverge. tanθ=yD Here, y is the...Chapter 38, Problem 1PQChapter 38, Problem 10PQChapter 38, Problem 31PQWrite the expression for the refraction at a spherical surface. nido+ntdi=(nt−ni)r (I) Here, ni is...Write the expression for spherical refracting surface. nid0+ntdi=nt−niR Here, d0 is the distance of...Chapter 38, Problem 76PQWrite the expression for focal length of a thin lens. 1f=1d0+1di1di=1f−1d0=d0−ffd0di=fd0d0−f Here,...Chapter 38, Problem 80PQWrite the expression for Snell’s law that relates the angle of incidence and angle of refraction of...Chapter 38, Problem 98PQWrite the expression for thin lens equation. 1f=1d0+1di Here, di is the distance of the image from...Write the expression for refraction law at left side of the given prism. sinθ1=nsinθ2 (I) Here, θ1...Write the expression for refraction law at left side of the given prism. sinθ1=nsinθ2 (I) Here, θ1...The Foucault pendulum does oscillation in the Earth’s reference frame, which is continuously...The speed of Desmond’s train is towards east. Write the formula for distance traveled in time t....Write the expression to obtain the Lorentz factor. γ=11−(vrelc)2 (I) Here, γ is the Lorentz factor,...Write the expression to obtain the position of the object along x axis in primed frame....Write the Lorentz’s transformation equations. y=y′ (I) t=γ(t′+vrelx′c2) (II) t′=γ(t−vrelxc2) (III)...Write the expression for the magnitude of velocity measured from the laboratory frame. v=vx2+vy2+vz2...Write relativistic kinetic energy equation of an electron. K=mc2−mrestc2 (I) Here, K is the kinetic...Write the expression for the rest mass energy. Erest=mrestc2 (I) Here, mrest is the rest mass,c is...Write the expression for the Lorentz constant. γ1=11−v12c2 Here, Lorentz constant is γ1, speed of...

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