Question

Problem 1 In the figure shown below, a solid sphere of radius a 3.90 cm is concentric with a spherical conducting shell of inner radius b 2.00a and outer radius c 2.40a. The sphere has a net uniform charge qi-+6.70 fC; the shell has a net charge q2- rd What is the magnitude of the electric field at radial distances (a) r -0 cm, (b) r - a/2.00, (c) r- a, (d) r-1.50a, (e) r 2.30a, and (f) r 3.50a? What is the net charge on the (g) inner and (h) outer surface of the shell? Problem 2 (a)What is the magnitude of an electron's acceleration in a uniform electric field of magnitude 1.87 x 106 N/C? (b)How long would the electron take, starting from rest, to attain 1/15-th the speed of light? (c)How far would it travel in that time?

Answer 1

Given that, Radius of the solid sphere(a) = 3.9cm charge(q) =+ 6.70fc = + 6.7 times 10^-15 C implies (a) r = 0 implies the electric field inside the sphere is E = k times Q times r/R^3 here r = 0 implies therefore E(r = 0) = 0 N/c implies (b) r = a/2 = 3.9/2 = 1.95cm implies E(1.95) = k times Q times r/R^3 = (9 times 10^9) times (6.7 times 10^-15)times (0.019)/(0.039)^3 = 0.019314 N/c therefore E(r = a/2) = 0.019314 N/c implies (c) r = a = 3.9cm E(3.9) = k times Q/r^2 = (9 times 10^9)times (6.7 times 10^-15)/(0.034)^2 = 0.05216 N/c therefore E(r = a) = 0.05216 N/c implies (d) r = 1.5a = 1.5 times (3.9) = 5.85cm E(5.85) = k times Q/r^2 = (9 times 10^9) times (6.7 times 10^-15)/(0.0585)^2 = 0.01762 N/c therefore E(r = 1.5a) = 0.01762 N/c implies till now the all points are inside shell so 'E' due to shell was zero implies charge of inner sphere has of = + 6.7fc
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