The electric field intensity at P and Q,in th | vedclass

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(C) The electric field at a point due to a charged spherical shell is given by $E = \frac{kQ}{r^2}$ for points outside the shell and $E = 0$ for point

Vedclass · Accepted Answer

$1: 1$

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(C) The electric field at a point due to a charged spherical shell is given by $E = \frac{kQ}{r^2}$ for points outside the shell and $E = 0$ for points inside the shell.For point $P$ (at distance $r$ from the center,which is outside the inner shell of charge $q$ and inside the outer shell of charge $3q$):$E_P = \frac{kq}{r^2} + 0 = \frac{kq}{r^2} \quad \dots (i)$For point $Q$ (at distance $2r$ from the center,which is outside both shells):$E_Q = \frac{kq}{(2r)^2} + \frac{k(3q)}{(2r)^2} = \frac{kq}{4r^2} + \frac{3kq}{4r^2} = \frac{4kq}{4r^2} = \frac{kq}{r^2} \quad \dots (ii)$Comparing $(i)$ and $(ii)$,the ratio of electric field intensities is:$E_P : E_Q = \frac{kq}{r^2} : \frac{kq}{r^2} = 1 : 1$.

The electric field intensity at $P$ and $Q$,in the shown arrangement,are in the ratio:

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