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  4. Two concentric conducting shells of radius a and b ( > a) carry charges Q and -2 Q, respectively. The correct variation of electric intensity E as a function of r is given by

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Q. Two concentric conducting shells of radius $a$ and $b$ $( > a)$ carry charges $Q$ and $-2 Q$, respectively. The correct variation of electric intensity $E$ as a function of $r$ is given by

Electric Charges and Fields

Solution:

The inner face of the outer shell has the charge $-Q$
and its outer face also has the charge $-Q$.
image
The final charge distribution on each face of shells is shown in figure. The expression for electric field is
given by $E=\frac{k Q}{r^{2}}$ for $a < r < b$ (radially outwards)
And $E=-\frac{k Q}{r^{2}}$ for $r > b $ (radially inwards)
Note that the field in the outward direction is assumed to be positive.