The figure shows two thin plastic spherical shells (shown in cross section) that

Question

The figure shows two thin plastic spherical shells (shown in cross section) that are uniformly charged. The center of the larger sphere is at < 0, 0, 0 >; it has a radius of 12 cm and a uniform positive charge of 7 x 10^-9 C. The center of the smaller sphere is at < 25, 0, 0 > cm; it has a radius of 3 cm and a uniform negative charge of -3x10^-9 C.

(a) What is the electric field at location A (6 cm to the right of the center of the large sphere)? Neglect the small contribution of the polarized molecules in the plastic, because the shells are very thin and don't contain much matter.

(b) What is the electric field at location B (15 cm above the center of the small sphere)? Again, neglect the small contribution of the polarized molecules in the plastic, because the shells are very thin and don't contain much matter.

(c) What is the force on an electron placed at location B?

Explanation / Answer

(a) You can treat the shells as two point charges when your field point is outside them. For part(a), you can disregard the large shell because point A is inside it, but you still need to count the charge from the small shell:

E = kq/r2 = (8.99 * 109 Nm2/C2)(3 * 10-9 C)/(0.19 m)2 = 7.4689 * 102 N/C directed in the positive x direction, so in vector notation E = 7.4689 * 102i N/C

(b) For part (b), you have a y component from the small shell:

E = (8.99 * 109 Nm2/C2)(3 * 10-9 C)(0.15 m)2 = -1.20 * 103j N/C

and both x and y components from the large shell (the distance is 0.29155 m from point B to the large shell)

Ex = (8.99 * 109 Nm2/C2)(7 * 10-9 C)(0.29155 m)2(0.25/0.29155) = 6.35 * 102 N/C

Ey = (8.99 * 109 Nm2/C2)(3 * 10-9 C)(0.29155 m)2(0.15/0.29155) = 3.81 * 102 N/C

so combining those we get the answer: E = 6.35 * 102i - 8.18 * 102 j N/C

(c) F = qE so force is -1.017 * 10-16i + 1.310 * 10-16j N

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