Two charged concentric spheres have radii of 0.10 m and 0.20 m. A charge of 50.0

Question

Two charged concentric spheres have radii of 0.10 m and 0.20 m. A charge of 50.0 nC is distributed evenly on the inner sphere. A charge q is distributed evenly on the outer sphere. The electric flux (E) through a spherical surface (r = 0.25 m) centered on the two charged spheres has a magnitude of 3950 Nm2 /C.

a) Determine all of the possible values of the charge, q, on the sphere of radius r = 0.20 m.

b) What properties of the electric field at the spherical surface at r = 0.25 m, allow us to use E = EA to relate the electric flux through the surface to the electric field on the surface?

Explanation / Answer

Here,

r1 = 0.10 m

r2 = 0.20 m

Q = 50 nC

flux = 3950 N.m^2/C

a)

let the charge is q

NOw, for the positive charge

(50 *10^-9 + q)/(8.854 *10^-12) = 3950

solving for q

q = -1.5 *10^-5 C

for negative flux

(50 *10^-9 + q)/(8.854 *10^-12) = -3950

q = -8.5 *10^-9 C

b)

as the electric field is in radial direction and the magnitude is constant over the whole sphere
it is always perpendicular to the area.

hence , we can write ,

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