Question

Consider a solid sphere with radius R with a charge uniformly spread throughout its volume. The magnitude of the sphere's electric field is |E_1| at a point P_1 on the sphere's surface and is |E_2| at a point P_2 at a distance 1/2R from the sphere's center. In the relationship |E_1| = b|E_2|, what is the value of b? A. 0 B. 1 C. 2 D. 4 E. 8 F. Other

Answer 1

on the surface

magnitude of electric field E1 = k*Q/R^2

at a distance r < R

consider a sphere of radius r < R

volume charge density sigma = Q/((4/3)*pi*R^3)

volume of sphere(r) V = (4/3)*pi*r^3

charge enclosed inside the sphere of radius r = Qin = sigma*V

Qin = Q*(r/R)^3

from gauss law

flux = Qin/e0

E2*A = Qin/eo

E2*4*pi*r^2 = Q*(r/R)^3

E2 = Q*r/(4*pi*e0*R^3) = k*Q*r/R^3

for r = R/2

E2 = k*Q/(2*R^2)

E2 = E1/2

E1 = 2*E2

E = b*E2

therefore b =2 <<< ----------ANSWER

OPTION (C)