An insulating sphere of radius 'R' having a cavity of radius R/4 at the periphery is charged uniformly with charge Q. The magnitude of electric field at point 'P' due to the above

Question

An insulating sphere of radius 'R' having a cavity of radius R/4 at the periphery is charged uniformly with charge Q. The magnitude of electric field at point 'P' due to the above charge distribution is 63 R 2 xkQ ​ then find x/8.

TestHub · Accepted Answer

Superpose a full sphere and a negative cavity: with the cavity removed the charge is Q, so the full sphere carries $\frac{64 Q}{63}$ and the cavity $- \frac{Q}{63}$ .

At P: $E = \frac{k ( 64 Q /63 )}{R ^{2}} - \frac{k ( Q /63 )}{( R /4 ) ^{2}} = \frac{64 - 16}{63} \cdot \frac{k Q}{R ^{2}} = \frac{48 k Q}{63 R ^{2}}$ .

So $x = 48$ and $\frac{x}{8} = 6$ .

Physics - Electrostatics Question with Solution | TestHub

Doubts & Discussion