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 +6 x 10-9 C. The center of the smaller sphere is at (28 cm, O); it has a radius of 3 cm and a uniform negative charge of -1 x 109 C. (a) What are the components E and EAy of the electric field E at location A (6 cm to the right of the center of the large sphere)? Neglect the small contribution of the pola 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.) N/C N/C

Explanation / Answer

given

Ra = 12 cm

Qa = 6*10^-9 C

location of smaller sphere = (28 cm, 0)

Rb = 3cm

Qb = -1*10^-9 C

a. E(A) = at r = 6 cm from origin

from gauss law

E = 0 V/m from spherre 1

E = kQb/0.22^2 from sphere 2

hence

Ex = 185.5371 V/m to the right

hence

total Ex = 185.53719 V/m

Ey = 0

b. for point B

electric field Ex due to both spheres = Ex

Ex = kQa*0.28/(0.28^2 + 0.15^2)^3/2 = 470.705062 V/m

similiarly

Ey = kQa*0.15/(0.28^2 + 0.15^2)^3/2 + kQb/0.15^2 = -146.9476 V/m

c. Fx = eEx ( e = 1.6*10^-19 C)

Fx = 753.1280992*10^-19 N

Fy = -235.11616*10^-19 N

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