In Prob. 2.25, you found the potential on the axis of a uniformlycharged disk:
(a) Use this, together with the fact that
(b) Find the potential for
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- Problem 2.21 Find the potential inside and outside a uniformly charged solid sphere whose radius is R and whose total charge is q. Use infinity as your reference point. Compute the gradient of V in each region, and check that it yields the correct field. Sketch V(r).arrow_forwardProblem 3.36 (3rd edition): Two long straight wires, carrying opposite uniform line charges +1, are situated on either side of a long conducting cylinder (Fig. 3.39). The cylinder (which carries no net charge) has radius R, and the wires are a distance "a" from the axis. Find the potential at point 7. (Hint: you can use solution of problem 2.47) R a aarrow_forwardA potential Vo(0) = k sin² (0/2) (k is a constant) is present on the surface of a hollow sphere ofradius R.1. Find the potential Vout(r, 0) outside the sphere (i.c., for r > R).arrow_forward
- Figure 2.12 Intersection of two conducting planes defining a corner in two dimensions with opening angle B. B.arrow_forwardProblem 2.11 Use Gauss's law to find the electric field inside and outside a spherical shell of radius R, which carries a uniform surface charge density o. Compare your answer to Prob. 2.7. Problem 2.21 Find the potential inside and outside a uniformly charged solid sphere whose radius is R and whose total charge is q. Use infinity as your reference point. Compute the gradient of V in each region, and check that it yields the correct field. Sketch V(r).arrow_forwardFigure 1.52 shows a spherical shell of charge, of radiusa and surface density σ, from which a small circular piece of radius b << a has been removed. What is the direction and magnitude of the field at the midpoint of the aperture? Solve this exercise using direct integration.arrow_forward
- Figure 2.72 For Prob. 2.8. 2.5 For the network graph in Fig. 2.69, find the number of nodes, branches, and loops.arrow_forwardFigure 1.52 shows a spherical shell of charge, of radius a and surface density σ, from which a small circular piece of radius b << a has been removed. What is the direction and magnitude of the field at the midpoint of the aperture? Solve this exercise using superposition.arrow_forwardFigure 1.52 shows a spherical shell of charge, of radius a and surface density σ, from which a small circular piece of radius b << a has been removed. What is the direction and magnitude of the field at the midpoint of the aperture? Solve this exercise in three ways: a) direct integration, b) by superposition, and c) using the relationship for a force on a small patch.arrow_forward
- Problem 2.22 Find the potential a distances from an infinitely long straight wire that carries a uniform line charge λ. Compute the gradient of your potential, and check that it yields the correct field.arrow_forward(Problem 4.10) A sphere of radius R carries a static radial polarization density P(r) = kr, r < R where k is a constant and r is the radial vector from the center of the sphere. (a) What are the dimensional units of the constant k? (b) Calculate the surface areal bound charge density o(R, 0, ø) and the volume bound charge density p(r). 2 (c) Find the electric field inside and outside the sphere.arrow_forwardSolve the shown integral and show is equal to one. prove it. please do then explain to me. thanks.arrow_forward
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