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A straight wire of length L carries a uniformly distributed charge Q. Find the electric field at a point P on its perpendicular bisector, where P is a distance a = (sqrt(3)/2)*L from the centre of the wire.

1. Q/(2*sqrt(3)*pi*epsilon0*L²)
2. sqrt(3)*Q/(4*pi*epsilon0*L²)
3. Q/(3*pi*epsilon0*L²)
4. Q/(4*pi*epsilon0*L²)

Correct answer: Q/(2*sqrt(3)*pi*epsilon0*L²)

Solution

For a finite line charge, the field on the perpendicular bisector is E = (lambda/(2*pi*epsilon0*a)) * sin(theta_max), where theta_max is measured from the perpendicular to the line joining P to the wire end. Substituting lambda = Q/L and the given geometry yields the result.

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