A charge Q accumulates on the hollow metallic dome,of radius R,of a Van de Graaff generator.A probe measures the electric field strength at various points outside the sphere surface.By what factor will the electric field value at the 2R distance be changed if the charge value were increased to (4/3)Q?

Question

Quizplus · Accepted Answer

The electric field outside a charged spherical shell is given by:

E = kQ/r^2

Where k is the Coulomb constant, Q is the charge on the shell, and r is the distance from the center of the shell.

Since we are interested in the electric field at 2R, we can substitute r=2R into the above equation and obtain:

E1 = kQ/(2R)^2 = kQ/4R^2

Now, if the charge on the shell is increased to (4/3)Q, the new electric field will be:

E2 = k(4/3)Q/(2R)^2 = (4/3)kQ/4R^2 = (4/3)E1

Therefore, the electric field at 2R distance will increase by a factor of 4/3. So the correct answer is B.

A Charge Q Accumulates on the Hollow Metallic Dome,of Radius