Aspherical cavity is hollowed out of the interior of aneutral conducting sphere. at the center of the cavity is a pointcharge, of positive charge q. a) what is the total surface charge q_int on the interior surface of the conductor (i. e., onthe wall of the cavity)? b) what is the magnitude e_int of the electric field inside the cavity as a function ofthe distance rfrom the point charge? let k, as usual, denote \frac{1}{4\pi\epsilon_0} .c) what is the electric field e_ext outside the conductor?

A) the total surface charge on the interior surface is equal in module to q+ and oposite in charge ().

B) The electric field inside the cavity is: .

C) The electric field outside the cavity is: .

Explanation:

The spherical cavity has a neutral charge. This means that this spherical cavity won´t affect the field inside. Therefore the field generated by the charge q+ is the same with or without the spherical cavity.

The total charge of the system can be calculated considering charge conservation:

Qtot0=Qtotf

q(+)=q(+)+qin+qex

qin=-qex and qin+qex=0

Using a Gaussian sphear centered in the charge q(+), we can calculate the field knowing that its direction would be .

If we apply the gaussian sphear between the interior and the exterior radius of the conducting hollow sphear, knowing that the field should be 0:

If we apply the gaussian sphear outside the exterior radius of the conducting hollow sphear, we obtain the field required in c).

pythagoras' theorem

square root (-5^2+9^2)

square root (25+81)

square root (106)

angle is tan^-1(9/5)

neg x, pos y