12.A point moves along a straight line OX so that its distance x cm. from the point O at time t sec. is given by the formula x = f - 6t + 9t . Find : i)at what times and in what positions the point will have zero velocity . ii) its acceleration at these instants. iii) its velocity when its acceleration is zero.
Q: Q3 In cylindrical coordinate system two conducting surfaces are located at Ø = 0 and 0 =n/2, and the…
A: Find the detailed solution in below images
Q: An hemispherical structure made of lead (o = 5x10 6) isotropic and homogeneous is charge-free. The…
A: a) The given data's are, Inner radius is a=20 cm, Outer radius is b=20+10=30 cm, Thickness is t=10…
Q: 1) Find the incremental field strength at P2 doe to the current element of 27 az µ Am at P The…
A:
Q: A thermally conducting solid bounded by two concentric spheres of radii a and b. a<b, is such that…
A: Given that the temperature of the inner surface is T1 The temperature of the outer surface is…
Q: D9.4. Let u 10-5 H/m, e = 4 x 10-9 F/m, o = 0, and p, = 0. Find k (including units) so that each of…
A: Given that Let 10-5 H/m₂ € = 4 x 10-⁹ F/m, o = 0, and p = 0. Find k = =(including units) so that…
Q: 1. A particle moves on the path y = 3.6x", where x and y are in meters. Its velocity has a constant…
A: Follow the notations provided in the solution
Q: Q1) The acceleration of a particle as it moves along a straight line is given by a = (2t -1) m/s',…
A: Given: A particle moving along a straight line a=2t-1 m/s2At t=0, s=1 m and v=2 m/s
Q: D9.4. Let u = 10-$ H/m, e = 4 x 10-9 F/m, o = (including units) so that each of the following pairs…
A: Given:μ=10-5 H/m∈=4×10-9 F/mσ=0ρv=0
Q: 11. A particle moves along the x-axis in such away that its distance x cm. from the origin after t…
A: Given, x=27t-2t 2 where, x is the distance in cm and t is the time in seconds.
Q: mx" + cx' + kx = F(t), x(0) = 0, x'(0) = 0 modeling the motion of a damped mass-spring system…
A: 2x''+8x'+80x=20e-t ;x0=0; x'0=0For the homogeneous part: xhAssume solution of form,…
Q: Q5/The electric field intensity in the region 0 <x < 1, 0< y<n/4,0 < z < 2 m in free space is given…
A:
Q: Exercise 1: 3y2 , Consider an electric field in the rectangular coordinates system 1) Find the…
A: Streamline The direction of velocity is determined by the streamline equation. The imaginary line or…
Q: с. Explain the significant physical difference between Poisson's and Laplace's equation? d. Find…
A: Electromagnetic theory
Q: 1. This first question contains a number of unrelated problems that should each be given a short…
A: Since it is not mentioned which question to attempt so considering the question number 1 given in…
Q: HOME WORK: Given the potential field in cylindrical coordinates, 100 r coso Volt, and point P at r =…
A: For the following potential field in cylindrical coordinates following is determined
Q: A wire 1.5 m long has a cross-sectional area of 2.4 m It is hung vertically stretches 0.32 mm when a…
A: Given, l =1.5 mA = 2.4 mm2∆l = 0.32 mm = 0.3210-3 mm = 10 kg ∑FY =0T-mg =0T-109.81 = 0T = 98.1…
Q: Q3) The acceleration of a particle traveling along a straight line is a = (8 - 2s) m/s', where s is…
A: Given, a=8-2s m/s2v=0 at s=0
Q: V is given by V = 50x2yz + 20y² in the free space, find (a) V at P(1,2,3) (b) E at P %3D
A:
Q: ompute for the potential, in millivolts, at P(9.16, 9.41, 9.03) if the potential at Q(9.46, 7.03,…
A: Given: P9.16,9.41,9.03,Q9.46,7.03,9.05VQ=0.76 Voltsλ 0,-8.72,-5.08=73.61 pC/m Required: VP
Q: We consider a cylinder of radius a whose length (orientated along the z axis) is very large with…
A: Consider a cylinder with radius a whose length (oriented along the z-axis) is very large with…
Q: 11.198 Perfectly conducting cylinders with radii of 8 mm and 20 mm are coaxial. The region between…
A: Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…
Q: Car A is traveling at a location where the speed limit is 100 km/h. The police officer in car P…
A: For car A, Speed of car A, vA=100 km/h=27.78 m/s uA=122 km/h=33.88 m/s Using the equation, v=u+at
Q: Given an electric potential of 1 q V= 4 πεο Γ find its corresponding electric field vector. Sol.…
A:
Q: Q2) The position of a particle along a straight line is given by s = (1.5t - 13.5ť + 22.5t) ft,…
A: Velocity: Velocity is vector quantity and have specified direction. It is the rate of change of…
Q: Show that the resistance requiredto achieve a heart rate H, in beats per minute, is given by the…
A: Write the expression for the time constant of the circuit. τ=RC
Q: (50 An electric field is given as E = () a, - 4a,. (a) Give the unit vector af in %3D cartesian…
A:
Q: A particle is moving on a straight line has acceleration a=5-3t and it's velocity=7 at time=2. If…
A: The solution is given below
Q: Q5 Coaxial Conducting cylinders located at r=4 cm and r= 16 cm. The region between cylinders is…
A:
Q: In a region where µ, = e,= 1 and o = 0, the retarded potentials are given by V = x(z – ct) V and A =…
A: In the question, we have μr=εr=1; σ=0. Also the retarded potential is given by V=xz-ctVA=xzc-taz…
Q: 9.22 i In a sourceless medium in which J = 0 and p, = 0, assume a rectangular coordinate system in…
A:
Q: 1.20 A coaxial cable has an inner radius a and an outer radius b. The space in between the…
A: Given a coaxial cable which has an inner radius a and outer radius b. The space in between the…
Q: A source free region is a region, where there is no net charge and no current. Show that in a…
A:
Q: A coaxial cable has voltage of 0.7 V on its inner conductor with a diameter of 4 cm and a voltage of…
A: Laplace equation for cylindrical coordinates is shown below. ∇2V=1ρ∂∂ρρ∂V∂ρ+1ρ2∂2V∂ϕ2+∂2V∂z2. We…
Q: 2. The surfaces p = 3 and 10 mm, and z = 0 and 25 cm are perfect conductors. The region enclosed by…
A: The detailed answer is solved below according to the given parameters and instructions in the…
Q: Q: Determine the field both inside and outside a spherical cloud of electrons with a uniform volume…
A: The figure drawn for the given condition is shown below: Where, i represents the inner surface and…
Q: Poisson's and Laplace's Equations Q5) Assume two conducting coes with their vertices on the origin…
A: Poisson and Laplace equation- A conductor has abundance of charge data free to move. When an…
Q: There are point loads ,Q1 = 9, Q2 = 3 and Q3 = 6 at points A(-6,0), O(0,0) and B (11,0) in the OXY…
A:
Q: A charged particle of mass 2 kg and charge 3 C starts at point (1, –2, 0) with velocity 4a, + 3a,…
A: As per our company guidelines we are supposed to answer only first one question. Kindly repost other…
Q: 10 Q5. Express -âg +RcosOâ, + â, in Cartesian coordinate system? Find Ē at (-3, 4, 0)? R
A:
Q: :V is given by V = 50x²yz + 20y² in the free space, find (a) V at P(1,2,3) (b) E at P
A:
Q: Q1) Given points in cylindrical system,: M(2, n, 0), N(1,0, 2),P(3, 7/2,1), find: (a) RMN; (b) rM|;…
A: If you want to get solution of some specific part then mention it but since i have to stick with the…
Q: Problem 5: The electric potential in Cartesian coordinates is given by V(x, y, z) = e- e-y+z?.…
A: Given: The potential in Cartesian coordinates is given by: Vx,y,z=ex-e-y+z2 To find: (a) The…
Q: Starting from the electric Gauss's law, derive the integral and differential forms of Maxwell's…
A: Aim- To derive and discuss the relationship between Maxwell 1stvequation and Gauss law for…
Q: The acceleration of a particle is given by a = 8t - 30, where a is in meters per second squared and…
A: Given data, Acceleration, a=8t-30 At t=0, s0=8 m At t=0, v0=0 m/s
Q: 1- Use time-varying Maxwell's equations to solve the following problem: a. Given H = 300 cos(3×10°t…
A: Answer -
Q: A mass spring system is given by the ODE: 2x′′ +cx′ +8(π^2)x=0 a) What are the values of c ≥ 0 for…
A: Given a O.D.E eqn. of mass spring system given by: 2x′′ +cx′ +8(π^2)x=0 For c≥0 we need to determine…
Q: Problem 8.5 Consider an infinite parallel-plate capacitor, with the lower plate (at z = -d/2)…
A: Solution- Consider an infinite parallel-plate capacitor, withThe lower plate at z=-d2 carrying…
Q: Q1) Write Maxwell's equations in differential, integral and phasor form, express the major…
A: Maxwell's equations are set of four complicated equations that describe the world of…
Step by step
Solved in 4 steps
- In the system shown in the figure below, the disk of inertia J and radius r is constrained tomove only about the stationary axis A. A viscous damping force of translational value fvexists between bodies J & M. If an external force f(t) is applied to the mass, find thetransfer function G(s) = Θ(s)/F(s)Application of Differential Equation A circuit has in series of electromotive force given by E(t) = 100 sin 60t V, a resistor of 2 Ω, an inductor of 0.1 H, and a capacitor of 1/260 farads. If the initial current and the initial charge on the capacitor are both zero coulombs, find the charge on the capacitor at any time t > 0.If the pole is located at the origin of the s plane, the response is in the form of a: a. damp exponential b. exponential rise c. sinusoid d. constant What characterizes an unstable system? a. poles at the origin b. poles with negative real part c. poles with positive real part d. poles without real part Routh’s stability criterion will provide the number of: a. RHP b. poles c. LHP d. imaginary poles
- Consider the continuous-time model of the overhead crane proposed in Problem 7.10 with mc = 1000 kg, ml = 1500 kg, and l = 8 m. Design a discrete full-order observer state feedback control to provide motion of the load without sway. Problem 7.10 The following differential equations represent a simplified model of an overhead crane:3 where mC is the mass of the trolley, mL is the mass of the hook/load, l is the rope length, g is the gravity acceleration, u is the force applied to the trolley, x1 is the position of the trolley, and x3 is the rope angle. Consider the position of the load y = x1 1 + sinx3 as the output. (a) Determine a linearized statespace model of the system about the equilibrium point x = 0 with state variables x1, x3, the first derivative of x1, and the first derivative of x3. (b) Determine a second statespace model when the sum of the trolley position and of the rope angle is substituted for the rope angle as a third state variable.Suppose a capacitor consists of two coaxial thin cylindrical conductors. The inner cylinder of radius ra has a charge of +Q, while the outer cylinder of radius rb has charge -Q. The electric field E at a radial distance r from the central axis is given by the function: E = αe-r/a0 + β/r + b0 where alpha (α), beta (β), a0 and b0 are constants. Find an expression for its capacitance. First, let us derive the potential difference Vab between the two conductors. The potential difference is related to the electric field by: V subscript a b end subscript equals integral subscript r subscript a end subscript superscript r subscript b end superscript E d r equals negative integral subscript r subscript b end subscript superscript r subscript a end superscript E d r Calculating the antiderivative or indefinite integral , Vab = (-αa0e-r/a0 + β+ b0 )right enclose blank end enclose subscript space r subscript a end subscript superscript space r subscript b end superscript By definition, the…Poisson's and Laplace's Equations Q5) Assume two conducting coes with their vertices on the origin and their axes on the z-axis. The point (2, 0, 4) is on the first cone (50 V) and the point (0, 6, 4) is on the second (10 V) cone, respectively. Find the voltage at (3, 4, 2).
- Continuity Equation and Relaxation Time Lightning strikes a dielectric sphere of radius 20 mm for which er εr = 2.5, σ= 5 x10-6 S/m and deposits uniformly a charge of 1 C. Determine the initial volume charge density and the volume charge density 2 μs later.hello, i’m studying coordinate system from electromagnetics. In the cartesian coordinate system, the coordinate variables x, y, and z are already length dimensions, so the scaling factors to convert them to length are hx=1, hy=1, and hz=1. In the cylindrical coordinate system, the scaling factors to convert the rho and z into length , are hrho=1 and hz=1. A) what is the hpi that changes coordinate pi into the length? B) in terms of spherical coordinates, what is the hr, htheta , hpi that changes ( r, theta, pi ) of spherical coordinate into the length?A cylindrical capacitor is made of two concentric conducting cylinders. The inner cylinder has radius R1 = 19 cm and carries a uniform charge per unit length of λ = 30 μC/m. The outer cylinder has radius R2 = 25 cm and carries an equal but opposite charge distribution as the inner cylinder. a. Use Gauss’ Law to write an equation for the electric field at a distance R1 < r < R2 from the center of the cylinders. Write your answer in terms of λ, r, and e0. E= b. Write an equation for the energy density due to the electric field between the cylinders in terms of λ, r, and e0. u = c. Consider a thin cylindrical shell of thickness dr and radius R1 < r < R2 that is concentric with the cylindrical capacitor. Write an equation for the total energy per unit length contained in the shell in terms of λ, r, dr, and ε0. dU/l = d. Calculate the energy stored per unit length in the capacitor in units of joules per meter. U/l = e. Calculate the electric potential difference between…
- Find the relative permittivity of the dielectric material present in a parallel-platecapacitor if: (a) S = 0.12 m/, d = 80 μm, V = 12 volt, and the capacitor contains1 ?? of energy; (b)The stored energy density is 100 ?/?/, V = 200 volt, and ? =45 ??; (c) ? = 200 ??/? and ?# = 20 ??/?/.A metal rod having a mass m and length l has resistance R. The rod hangs from two vertical metallic wires of length l in a uniform vertical magnetic field B of a horseshoe magnet (see figure). The wires have negligible resistance. An AC voltage source is connected between the wires which provides a voltage U(t) = U0 cos ωt, where U0 and ω are constants. a) Show that for small angular displacements φ the motion of the rod can be described by the equation U(t) = αφ ̈ + βφ ̇ + γφ, and express the constants α, β, γ in terms of quantities m, l, B, R and the gravitational acceleration g. b) At a certain frequency ω = ω0 the amplitude of the oscillations of the rod becomes large and the equation above does not describe themotion anymore. Estimate the frequency ω0.An infinitely large flat surface has a surface density of electric charge. The surface moves with constant velocity in a parallel direction. Show that the differential version of the Poynting theorem holds at all points above and below the surface.