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A semicircular wire of radius R with linear charge density lambda1 and a straight wire (the diameter of the semicircle) with linear charge density lambda2 are arranged so that their center is at point C. Find the ratio lambda1/lambda2 such that the net electric field at C points only along the y-axis.
- 1/2
- 2/pi
- pi/2
- 2
Correct answer: pi/2
Solution
The semicircle gives a field of magnitude 2k*lambda1/R in the -y direction. A finite straight wire of length 2R at its midpoint gives a field (perpendicular to the wire) of 2k*lambda2/(R) in the y-direction... setting their sum to zero along x and matching y-components gives lambda1/lambda2 = pi/2.
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