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A ring of charge with radius 0.5 m has $0.002 π m$ gap. If the ring carries a charge of + 1 C, the electric field at the center is nearly

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$6.2 \times 10^{7} N C^{- 1}$

$7.5 \times 10^{7} N C^{- 1}$

$6.5 \times 10^{7} N C^{- 1}$

$7.2 \times 10^{7} N C^{- 1}$

answer is B.

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Detailed Solution

Charge on the element opposite to the gap is

$d q = \frac{Q}{2 π r} (0.002 π)$ $= \frac{1}{2 π (0.5)} = = \frac{2 π}{1000} = 2 \times 10^{- 3} C$

$E = \frac{d q}{4 π ε_{0} r^{2}}$ $= \frac{9 \times 10^{9} \times 2 \times 10^{- 3}}{(0.5)^{2}} = 7.2 \times 10^{7} {NC}^{- 1}$

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