question_answer

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

A) \[7.5\times {{10}^{7}}N{{C}^{-1}}\]

B)        \[7.2\times {{10}^{7}}N{{C}^{-1}}\]

C) \[6.2\times {{10}^{7}}N{{C}^{-1}}\]

D)        \[6.5\times {{10}^{7}}N{{C}^{-1}}\]

Correct Answer: B

Solution :

[b] Charge on the element opposite to the gap is \[dq=\frac{Q}{2\pi r}\left( 0.002\pi  \right)\] \[=\frac{1}{2\pi \left( 0.5 \right)}\times \frac{2\pi }{1000}=2\times {{10}^{-3}}C\] \[E=\frac{9\times {{10}^{9}}\times 2\times {{10}^{-3}}}{{{\left( 0.5 \right)}^{2}}}=7.2\times {{10}^{7}}N{{C}^{-1}}\]