For a uniformly charged spherical sphere of radius R carrying a total charge Q,calculate the electric field at a distance R/2 outside the sphere divided by the electric field at a distance R/2 inside the sphere.
A)9/8
B)infinity
C)4/9
D)8.0
E)8/9

Question

Quizplus · Accepted Answer

For a uniformly charged spherical sphere, the electric field outside the sphere is given by:

E = kQ/r^2

where k is Coulomb's constant, Q is the total charge, and r is the distance from the center of the sphere.

At a distance R/2 outside the sphere:

E_outside = kQ/(R/2)^2 = 4kQ/R^2

Inside the sphere, the electric field is:

E_inside = kQr/R^3

where r is the distance from the center of the sphere. At a distance R/2 inside the sphere,

r = R/2

E_inside = kQ(R/2)/R^3 = kQ/2R^2

Now, we can calculate the ratio of the fields:

E_outside/E_inside = (4kQ/R^2)/(kQ/2R^2) = 8/1 = 8

Therefore, the answer is E) 8/9.

For a Uniformly Charged Spherical Sphere of Radius R Carrying