Answer 1

The magnitude of electric flux through a closed surface is,

Here, is the electric field and is the area.

The magnitude of electric flux through a closed surface is,

For maximum flux, the angle must be equal to . The Gaussian surface due to the point charge is a sphere.

Substitute for and for A.

So the electric flux is,

Gauss law states that the electric flux through a closed surface is proportional to times the charge enclosed in it and is given by,

Here, q is the charge and is the permittivity.

Substitute for in .

Rearrange the equation for the charge.

The charge on the metal sphere is,

Substitute for E, for , and 3.50 cm for r.

The electric field is directed away from the charge if the charge is positive and is directed towards the charge if the charge is negative.

Here, the electric field is directed towards the metal ball. So, the charge is negative.

Therefore, the charge that resides on the ball is .