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Find the electric field at the point P (as shown in the figure) on the perpendicular bisector of a uniformly charged thin wire of length L carrying a charge Q. The distance of the point P from the centre of the rod is a=(√3)/2L. [the rod stands vertically with its midpoint O, and P lies on the horizontal line through O at a distance a from it]

Asked in JEE Main 26th Feb 1st Shift 2021 · Rod and line charge

• (1) Q/(3πε₀ L²)
• (2) (√3 Q)/(4πε₀ L²)
• (3) Q/(4πε₀ L²)
• (4) Q/(2√3 πε₀ L²)

Step-by-step solution

Why the other options are wrong

• (1) Drops the factor 1/(√3) that comes from a=(√3)/2L in the denominator, leaving (2kQ)/(L²)·2/3 instead of (2kQ)/(√3 L²).
• (2) Not reachable by one slip: this is 3/2 times the key, whereas putting √3 in the numerator instead of the denominator gives (√3 Q)/(2πε₀L²), twice as large.
• (3) Treats the rod as a point charge at distance L, ignoring both the finite length and the actual value of a.

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