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

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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

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$7.5 \times 10^{7} {NC}^{- 1}$

$7.2 \times 10^{7} {NC}^{- 1}$

$6.2 \times 10^{7} {NC}^{- 1}$

$6.5 \times 10^{7} {NC}^{- 1}$

answer is B.

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Detailed Solution

Charge on the element opposite to the gap is

$\begin{array}{l} d q = \frac{Q}{2 π r} (0.002 π) \\ \Rightarrow d q = \frac{1}{2 π (0.5)} \times \frac{2 π}{1000} = 2 \times 10^{- 3} C \\ ∴ E = \frac{k q}{r^{2}} = \frac{9 \times 10^{9} \times 2 \times 10^{- 3}}{(0.5)^{2}} = 7.2 \times 10^{7} {NC}^{- 1} \end{array}$