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You are a coach for the Physics Olympics team participating in a competition overseas. You are given the following sample problem to present to your team of students, which you need to solve very quickly: A person is standing on the midline of a soccer field. At one end of the field, as shown in Figure P24.28, is a letter D, consisting of a semicircular metallic ring of radius R and a long straight metal rod of length 2R, the diameter of the ring. The plane of the ring is perpendicular to the ground and perpendicular to the midline of the field shown by the broken line in Figure P24.28. Because of an approaching lightning storm, the semicircular ring and the rod become charged. The ring and the rod each attain a charge Q. What is the electric potential at point P, which is at a position x along the midline of the field, measured from the center of the rod, due to the letter D? Think quickly and use all resources available to you, which include your physics textbook: yon are in competition!
Figure P24.28
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Chapter 24 Solutions
PHYSICS FOR SCI.AND ENGR W/WEBASSIGN
- 04. a. A control volume is an arbitrary volume of space through which fluid can flow. Let the control volume of a spherical shaped blob in a flowing fluid is V. Suppose the fluid has density p(r, t) and velocity field u. Then applying mass conservation to the blob, Rate of change of mass in=- Mass out flow. The total mass of fluid entering to the blob in a control volume V is We a The mass out flow is given by, m = p dv. ff (PL) (pu) ds where, S is the surface bounded by the control volume V. Apply the Gauss Divergence Theorem to show that, др at -+V. (pu) = 0.arrow_forwardA simple and common technique for accelerating electrons is shown in the figure, which depicts a uniform electric field between two plates. Electrons are released, usually from a hot filament, near the negative plate, and there is a small hole in the positive plate that allows the electrons to pass through. Randomized Variables E = 2.7 × 104 N/C Calculate the horizontal component of the electron's acceleration if the field strength is 2.7 × 104 N/C. Express your answer in meters per second squared, and assume the electric field is pointing in the negative x-direction as shown in the figure.arrow_forwardScientists in the laboratory create a uniform electric field E-9.0x105 k V/m in a region of space where B = 0. ▼ Part A What are the components of the electric field in the reference frame of a rocket traveling in the positive x-direction at 1.4x108 m/s ? Express your answer using two significant figures separated by commas. Ex, Ey, Ez = 0,0,9.0x105 V/m Submit Previous Answers Correct Part B What are the components of the magnetic field in the reference frame of the rocket? Express your answer using two significant figures separated by commas. VE ΑΣΦ B₂, By, B₂= 0,0, 1.4 10 ● Submit Previous Answers Request Answer X Incorrect; Try Again; One attempt remaining ? Tarrow_forward
- A long cylinder of charge q has a radius a. The charge density within its volume, p, is uniform (Figure). Describe the form of the electric field generated by the cylinder. Find the electric field strength at a distance r from the axis of the cylinder in the regions (i) r > a and (ii) 0 <r<a.If a non-relativistic electron moves in a circle at a constant distance R from the axis of the cylinder, where R > a, find an expression for its speed.arrow_forwarda. Given that D=10xa,cm2 ,determine the flux crossing a 1 m? area that is normal to the axis at x = Зт.arrow_forwardIn a given region of empty space, By = B0 * e-t / T (where B0 and T are constants), but Bx and Bz are constant in time. a. What is the magnitude and direction of the electric curl of that region in terms of B0, T, and time t? b. Assume that Evector always points in the +x direction and is zero at z = 0. Find Ex as a function of position and time. [Hint: the answer is B0 * e-t / T * (z / T) + C] c. Check that the units of your expression make sense.arrow_forward
- An electron has an initial velocity of 2.4x106 m/s in the +x direction. It enters a uniform electric field E = 397 N/C which is in the +y direction. What is the ratio of the y-component of the velocity of the electron to the x-component of the velocity after traveling 5 cm in the +x direction in the field? (Your result must include 2 digit after the decimal point and maximum of 5% of error is accepted in your answer. Take elementary charge 1.6x10-19 C and take mass of electron 9.1x10-31 kg.)arrow_forwardProblem 31.31 An electron travels with = 4.00 x 106 m/s through a point in space where E=(2.10 x 105-2.10 x 105) V/m and B = -0.130 T. Part A What is the force on the electron? Express vector F in the form Fz, Fy, where the x and y components in newtons are separated by a comma. F. ΕΧΕΙ ΑΣΦ ? N Submit Request Answer Provide Feedback 12 of 14 He Review Next >arrow_forwardSuppose 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 rp has charge -Q. The electric field E at a radial distance r from the central axis is given by the function: E = ae-T/ao + B/r + bo where alpha (a), beta (8), ao and bo are constants. Find an expression for its capacitance. First, let us derive the potential difference Vah between the two conductors. The potential difference is related to the electric field by: Vab = Edr = - Edr Calculating the antiderivative or indefinite integral, Vab = (-aage-r/a0 + B + bo By definition, the capacitance Cis related to the charge and potential difference by: C = Evaluating with the upper and lower limits of integration for Vab, then simplifying: C= Q/( (e-rb/ao - eTalao) + B In( ) + bo ( ))arrow_forward
- Using the symmetry of the arrangement, determine the direction of the force on +q in the figure below, given that: Case I. qa=qb= +6.5 μC and qc = qd = +6.5 μC. (a) In your notebook, draw the forces on q due to qar qb²9c² (b) Due to symmetry the direction of the net force is F O qc net ✔N O qd Hint: For each force draw the x and y components. Some will add and some will cancel. (c) Calculate the magnitude of the force on the charge q, given that the square is 10.0 cm on a side and q = 2.3 μC. and 9d- Xarrow_forwardInside a vacuum tube, an electron is projected between two parallel Problem 1 plates. The plates are separated by 3 cm and are 10 cm long. Equal but opposite electric charges are placed on the plates, so that there is a uniform electric field between the plates and no field outside of the plates. The electron is projected in the center of the positive plate and its initial velocity is 4.5 x 10 m/s straight towards the center of the negative plate. Find the magnitude of the electric field such that the electron just barely misses touching the negative plate before it turns around goes directly back out of the hole. 10cm. Зстarrow_forwardTwo 16 cm -long thin glass rods uniformly charged to +16nC are placed side by side, 4.0 cm apart. What, are the electric field strengths E₁, E2, and E3 at distances 1.0 cm, 2.0 cm, and 3.0 cm to the right of the rod on the left, along the line connecting the midpoints of the two rods? Part C Specify the electric field strength E3. Express your answer to two significant figures and include the appropriate units. E3 μà -1.2.105 Review | Constants N C S Submit Previous Answers Request Answer Provide Feedback X Incorrect; Try Again; 4 attempts remaining Next >arrow_forward
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