Question

3. A solid spherical insulator with radius Ry is surrounded by a conducting spherical shell with inner radius R2 and outer radius R3 and with the same center point as the central sphere. The central sphere has charge density p yr3, where r is the distance from the common center of the sphere and shell. The conducting shell has charge Q. Find the magnitude of the electric field as a function of r in the following regions: R2 (a)r s R (b) R1 <r< R2 (c) R2 <r< R3 (d) R3 < r. Express your answers in terms of Ri, Q-Y, r and εο ork.

Answer 1

Here we will use Gauss law to find Electric field.

(a) R < R_1 e = Yr^3 we will use Gaw's Law integral E.dr = q_in/sigma_0 (E) (4 pi r^2) = integral^r_0 s (4 pi r^2) dr/sigma_0 (E) (4 pi r^2) = y4 pi [r^6/6]^r_0/sigma_0 E = y r^6/6 sigma)0 r^2 E = y r^4/6 sigma)0 \r\n (b) R_1 < r < R_2 So here we have to find not change in the inner solid sphere. Q_net = integral^R_1_0 S(s pi r^2)dr = 4 pi y R^6_1/6 E = kq_net/r^2 = 1/a pi sigma_0 2/3 pi Y R^6_1/r^2 (c) R_2 < r < R_3 E = kq_net/r^2, q_net = 4 pi yR^6_1/6 E = pi YR^6_1/6 pi sigma_0 r^2 (d) R_3 < r E = 1/4 pi sigma_0 (Q + 4 pi YR^6_1/6/R^2