# Two spherical cavities, of radii a and b, are hollowed out from the interior of a (neutral)...

## Question:

Two spherical cavities, of radii {eq}a {/eq} and {eq}b {/eq}, are hollowed out from the interior of a (neutral) conducting sphere of radius {eq}R {/eq}. At the center of each cavity a point charge is placed; call these charges {eq}q_a {/eq} and {eq}q_b {/eq}.

(a) Find the surface charges {eq}\sigma_a {/eq}, {eq}\sigma_b {/eq}, and {eq}\sigma_R {/eq}.

(b) What is the field outside the conductor?

(c) What is the field within each cavity?

(d) What is the force on {eq}q_a {/eq} and {eq}q_b {/eq}?

(e) Which of these answers would change if a third charge, {eq}q_c {/eq}, were brought near the conductor?

## The Electric Field Inside Conductor with Cavities:

We know that the electric field inside a conductor is zero. Things are different for a conductor having cavities. If the cavity contains a charge, then the electric field inside the cavity will not be zero although the total field inside the conductor remains zero. The change inside the cavity will induce an equal and opposite amount of charge on the boundary of the cavity.

a). Charge {eq}q_{a} {/eq} will induce an equal and opposite charge on the surface of the cavity. The charge density is then, , {eq}\displaystyle...

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