Two thin plastic spherical shells (shown in cross section in the figure below) a

Question

Two thin plastic spherical shells (shown in cross section in the figure below) are uniformly charged. The center of the larger sphere is at (0, 0); it has a radius of 12 cm and a uniform positive charge of +3 109 C. The center of the smaller sphere is at (29 cm, 0); it has a radius of 3 cm and a uniform negative charge of 4 109 C. I only need parts B and C, part A is correct.

(a) What are the components EA,x and EA,y of the electric field

(b) What are the components EB,x and EB,y of the electric field at location B (15 cm above the center of the small sphere)? Neglect the small contribution of the polarized molecules in the plastic, because the shells are very thin and don't contain much matter. (Indicate the direction with the sign of your answer.)

(c) What are the components Fx and Fy of the force on an electron placed at location B? (Indicate the direction with the sign of your answer.)

Explanation / Answer

(b)
Electric Field at B due to smaller sphere,
Ebx1 = 0
Eby1 = k*Q/r^2
Eby1 = (8.9*10^9 * 3*10^-9)/(0.15)^2
Eby1 = -1186.1 j^ N/C

Distance btw A & B = sqrt (29^2 + 15^2) = 32.65 cm

Electric Field at A due to smaller sphere,
Ebx2 = k*Q/r^2 * 29/32.65
Ebx2 = (8.9*10^9 * 3*10^-9)/(0.3265)^2 * 29/32.65
Ebx2 = + 222.46 i^ N/C

Eby2 = k*Q/r^2 * 15/32.65
Eby2 = (8.9*10^9 * 3*10^-9)/(0.3265)^2 * 15/32.65
Eby2 = 115.06 j^ N/C

Net Electric Fiel components,
Ebx = Ebx1 + Ebx2
Ebx = 222.46 N/C

Eby = Eby1 + Eby2
Eby = - 1186.1 + 115.06

Eby = - 1071 N/C

(C)
Force on an electron,
Fx = q* E
Fx = 1.6 * 10^-19 * 222.46

Fx = - 3.55 * 10^-17 N

Fy = q* E
Fy = 1.6 * 10^-19 * 714.4
Fy = 1.1713 * 10^-16 N

-ve sign means towards -ve axis.
+ve sign means towards +ve axis.

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