Two plastic spheres The figure shows two thin plastic spherical shells shown in

Question

Two plastic spheres The figure shows two thin plastic spherical shells shown in cross section that are uniformly charged The center of he ar er ere s at ) > as a radius of cm and a uniform positive charge of 6 x 109 C. The center of the smaller sphere is at cm; it has a radius of 3 cm and a uniform negative charge of -3 x 10-9 C (a) What Is the electric fleld at locatlon A (6 cm to the rlght of the center of the large sphere)? Neglect the small contrlbutlon of the polarized molecules In the plastic, because the shells are very thin and don't contaln much matter. > N/C (b) What is the electric field at location B (15 cm above the center of the small sphee) Again, neglect the small contribution of the polarized molecules in the plastic, because the shells are very thin and don't contain much matter. N/C (c) What is the force on an electron placed at location B? >N

Explanation / Answer

given two plastic spherical shells
Center of larger sphere is at origin
Radius of larger sphere R1 = 12 cm = 0.12 m
Charge on larger sphere, Q1 = 6*10^-9 C
Radius of smaller sphere, R2 = 0.03 m
Charge, Q2 = -3*10^-9 C
distance between spheres, d = 0.25 m

a. electric field at point A = Ea
   consider a gaussean surface , spherical, centered at origin, of radius r = 6 cm
   then E*4*pi*r^2 = qen/epsilon ( from gauss' law)
   but qen = 0
   so E = 0
   E = (0,0,0) N/C

b. Electric field at B = Eb
   Eb = kQ2 j / 0.15^2 + kQ1(di + 0.15j)/(0.15^2 + d^2)^3/2 [ i and j are unit vectros in x and y directions, and we are adding contributions of both the spheres considering them as point charges placed at their centers]
   Eb = 8.98*10^9(-3*10^-9) j / 0.15^2 + 8.98*10^9*6*10^-9(0.25i + 0.15j)/(0.15^2 + 0.25^2)^3/2
   Eb = 543.549i - 871.20322 j
   Eb = (543.549, - 871.203,0) N/C

c. Net force on elkectron placed at B F = qEb
   (-1.6*10^-19)((543.549, - 871.203,0))
   F = (-8.6967*10^-17, 1.3939*10^-16, 0) N

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