A uniformly charged wire of linear charge density λ is bent into a U-shape. It consists of a semicircular arc of radius R joined tangentially at its two ends to two semi-infinite parallel straight portions extending to the right. O is the centre of the semicircle. The electric field at O is:
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Question

A uniformly charged wire of linear charge density λ is bent into a U-shape. It consists of a semicircular arc of radius R joined tangentially at its two ends to two semi-infinite parallel straight portions extending to the right. O is the centre of the semicircle. The electric field at O is:

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G1 Physics · Accepted Answer

The semicircular arc produces E a r c E_arc E a ​ r c = 2kλ/R toward the open side. Each semi-infinite straight part contributes an x-component kλ/R in the opposite direction. Their y-components cancel. Hence, E l i n e s E_lines E l ​ in es = 2kλ/R, opposite to E a r c . E_arc. E a ​ r c . Therefore, E n e t E_net E n ​ e t = 0.