Two concentric spheres are shown in Fig. 22.9. The inner sphere is a solid nonco

Question

Two concentric spheres are shown in Fig. 22.9. The inner sphere is a solid nonconductor and carries a charge of +5.00 mu C uniformly distributed over its outer surface. The outer sphere is a conducting shell that carries a net charge of -8.00 mu C. No other charges are present. The radii shown in the figure have the values R_1 = 10.0 cm, R_2 = 20.0 cm, and R_3 = 30.0 cm. (a) Find the total excess charge on the inner and outer surfaces of the conducting sphere. (b) Find the magnitude and direction of the electric field at the following distances r from the center of the inner sphere: (i) r = 9.5 cm, (ii) r = 15.0 cm, (iii) r = 270 cm, (iv) r-35.0 cm. A) a) -3.00 mu C (inner surface), -5.00 mu C (outer surface): (b) (i) 0: (ii) 2.00 times 10^6 N/C, radially outward: (iii) 0: (iv) 2.20 times 10^5 N/C, radially inward B) (a)-5.00 mu C (inner surface), -3.00 mu C (outer surface): (b) (i) 0: (ii) 2.00 times 10^6 N/C, radially outward: (iii) 0: (iv) 2.20 times 10^5 N/C, radially inward C) a) 3.00 mu C(inner surface), 5.00 mu C (outer surface. (b) (i) 0: (ii) 220 times 10^6 N/C, radially outward: (iii) 0: (iv) 2.20 times 10^5 N/C, radially inward

Explanation / Answer

(a)

charge in the inner surface is

Qin = 5 uC

change in the outer surface is

Q out = -8 uc+ 5 uc = - 3 uC

(B)

electric field due to point charge is

E = kq/r^2

at r = 9.5 cm

E = 0

at r = 15 cm

E = 9* 10^9 ( 5* 10^-6)/(0.15)^2

=2.0 * 10^6 N/C( radiallt ouward)

at r= 27 cm

E = 0

at r= 35

E = 9* 10^9 ( 3* 10^-6)/(0.35)^2

=2.2 * 10^5N/C( radiallt inward)

option (B) is correct answer

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