A neutral conductor contains a hollow cavity in which there is a$+100\mathrm{nC}$point charge. A charged rod then transfers$-50\mathrm{nC}$ to the conductor. Afterward, what is the charge (a) on the inner wall of the cavity, and (b) on the exterior surface of the conductor?

(a).

Figure$1$for charge on the cavity's inner wall is shown below,

(a).

Even though there is a positive charge $+100\mathrm{nC}$in the cavity, the electric field inside any conductor is zero.

As demonstrated figurelocalid="1648723570245" $1$,thelocalid="1648722160266" $+100\mathrm{nC}$inside the cavity creates a negative charge of the same magnitude on the cavity's inner surface.

As a result, the charge on the cavity's inner surface is the same magnitude as the charge within, but in the opposite direction.

So,

$\mathrm{Q}=-100\mathrm{nC}$

(b).

Figure$2$for charge on the exterior surface of the conductor shown below,

(b).

The initial charge on the conductor's surface is$+100\mathrm{nC}$before conducting the rod, as indicated in the figure$2$.

This happens because the negative charge on the cavity's inner surface produces a positive charge on the conductor's external surface to keep it neutral.

The negative charge transfers to the outside surface after conducting the rod at$50\mathrm{nC}$.

The net charge becomes,

$\mathrm{Q}=+100\mathrm{nC}+(-50\mathrm{nC})=+50\mathrm{nC}$