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Two infinite plane sheets, each carrying uniform surface charge density +sigma, are arranged so that the angle between them is 30 deg. Find the electric field in the wedge-shaped region between them (orientation as shown in the figure).

1. sigma/e0 [(1 + sqrt(3)/2) yhat + xhat/2]
2. sigma/(2 e0) [(1 - sqrt(3)/2) yhat - xhat/2]
3. sigma/(2 e0) [(1 + sqrt(3)) yhat + xhat/2]
4. sigma/(2 e0) [(1 + sqrt(3)) yhat - xhat/2]

Correct answer: sigma/(2 e0) [(1 + sqrt(3)) yhat - xhat/2]

Solution

One sheet (horizontal) contributes sigma/(2e0) along +y. The tilted sheet's normal makes 30 deg with the vertical, giving components sigma/(2e0)*cos30 = sigma sqrt(3)/(4 e0) along y and -sigma/(2e0)*sin30 = -sigma/(4e0) along x. Summing yields sigma/(2e0)[(1 + sqrt(3)) yhat - xhat/2] for the configuration shown.

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