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 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 -3 10-9 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.
< 1 ., 2 ., 3 .> N/C
(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.
< 4 ., 5 ., 6 .> N/C
(c) What is the force on an electron placed at location B?
< 7 , 8 , 9 .> N

Explanation / Answer

(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.

Acording to the gauss's law, electric field inside a shell is zero.

E = 0

(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.

E1 = q1/4??r^2

r = ?(25*25+15*15) = 29.155 cm

E1 = q1/4??r^2 = 4e-9/(4*3.1416*8.85e-12*0.29155*0.29155) = 423.14 N/C

E1_x = E1 (25/ 29.155) = 423.14*(25/ 29.155) = 362.84 N/C

E1_y = E1 (15/29.155) = 423.14*(15/29.155) = 217.70 N/C

E2 = q2/4??r^2 = 3e-9/(4*3.1416*8.85e-12*0.15*0.15) = 1198.9 N/C

E2_x = 0

E2_y = -1198.9 N/C

E_x = E1_x + E2_x = 362.84+ 0 =362.84

E_y = E1_y + E2_y = 217.70- 1198.9 = -981.2 N/C

E = ?((E_x)^2+(E_Y)^2) = ?(362.84*362.84+ 981.2*981.2) =1046 N/C

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

F = qE = 1.6e-19 * 1046 =1.67e-16 N

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