A ring of charge with radius R = 0.5, m havin | vedclass

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(B) The electric field at the centre of a complete ring is zero. If we have a ring with a small gap,the field at the centre is equivalent to the field

Vedclass · Accepted Answer

$2.31	imes10^8\, N/C$

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(B) The electric field at the centre of a complete ring is zero. If we have a ring with a small gap,the field at the centre is equivalent to the field produced by the charge that would have occupied the gap,but with the opposite sign.The linear charge density is $\lambda = \frac{Q}{2\pi R - l}$.The charge in the gap of length $l$ is $q = \lambda l = \frac{Q l}{2\pi R - l}$.Given $Q = 1\, C$,$R = 0.5\, m$,and $l = 0.02\, m$:$q = \frac{1 	imes 0.02}{2 	imes 3.14159 	imes 0.5 - 0.02} = \frac{0.02}{3.14159 - 0.02} \approx \frac{0.02}{3.12159} \approx 0.0064\, C$.The electric field at the centre due to this small segment is $E = \frac{k q}{R^2} = \frac{9 	imes 10^9 	imes 0.0064}{(0.5)^2} = \frac{5.76 	imes 10^7}{0.25} = 2.304 	imes 10^8\, N/C \approx 2.31 	imes 10^8\, N/C$.

$A$ ring of charge with radius $R = 0.5\, m$ having a gap of length $l = 0.02\, m$,carries a total charge of $Q = +1\, C$. The electric field at the centre is

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