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  4. A hollow metal ball 8 cm in diameter is given a charge -4× 10-8C. The potential on the surface of the ball is

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Q. A hollow metal ball $8 \,cm$ in diameter is given a charge $ -4\times 10^{-8}C. $ The potential on the surface of the ball is

AMUAMU 2003

Solution:

The potential on the surface of a ball of radius $R$, is given by
$V=\frac{1}{4 \pi \varepsilon_{0}} \cdot \frac{Q}{R}$
Given, $R=\frac{8}{2} cm =\frac{8}{2} \times 10^{-2} m$,
$=4 \times 10^{-2} m $
$Q =-4 \times 10^{-8} C$
$V =9 \times 10^{9} \times \frac{-4 \times 10^{-8}}{4 \times 10^{-2}} $
$=-9000$ volt