Uniformly Charged Rod PYQ | Find Force on a Point Charge | JEE Main Physics

Find Force on a Charge Due to a Uniformly Charged Rod | JEE Main 2026 (January)

This problem is based on the concept of Electric Field due to a Uniformly Charged Rod. Instead of finding the electric field by integration, we directly use the standard result for the electric field on the axis of a uniformly charged rod. Finally, the force on the given charge is calculated using F = qE.

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Question

A uniformly charged rod has:

• Total Charge, Q = 2 μC
• Length, L = 10 cm
• A point charge, q = 1 μC, is placed 2 cm from one end of the rod.

Find the force acting on the charge.

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Given Data

• Total charge on rod, Q = 2 × 10^-6 C
• Point charge, q = 1 × 10^-6 C
• Length of rod, L = 10 cm = 0.10 m
• Distance from rod, a = 2 cm = 0.02 m
• Coulomb's Constant, k = 9 × 10⁹ N·m²/C²

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Concept Used

The electric field at a point located on the extension of a uniformly charged rod is given by

E = kQ / [a(L + a)]

where,

• Q = Total charge on the rod
• L = Length of the rod
• a = Distance of the point from the nearer end of the rod

Once the electric field is known, the force on the charge is

F = qE

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Step 1: Calculate Electric Field

Using

E = kQ / [a(L+a)]

Substitute the values:

E = (9 × 10⁹) × (2 × 10^-6) / [(0.02)(0.12)]

Since,

0.02 × 0.12 = 0.0024

Therefore,

E = 1.8 × 10⁴ / 0.0024

E = 7.5 × 10⁶ N/C

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Step 2: Calculate Force

Using

F = qE

Substitute the values:

F = (1 × 10^-6) × (7.5 × 10⁶)

F = 7.5 N

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Final Answer

Force acting on the charge = 7.5 N

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Important Formula

Electric Field due to Uniformly Charged Rod:

E = kQ / [a(L+a)]

Force on a Charge:

F = qE

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Quick Revision

• Uniformly charged rods produce a non-uniform electric field.
• Always convert centimeters into meters before calculation.
• First calculate the electric field, then multiply by the point charge.
• For a positive rod and positive charge, the force is repulsive.
• The SI unit of electric field is N/C.
• The SI unit of force is Newton (N).

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Exam Tips

• Remember the standard formula for the electric field on the axis of a uniformly charged rod.
• Do not use Coulomb's law for the entire rod as if it were a point charge.
• Keep all quantities in SI units before substitution.
• After finding the electric field, use F = qE directly.
• These direct formula-based questions are frequently asked in JEE Main.