JEE Main · 2023 · 24 Jan 2023 · Shift 1 · Magnetic Effects of Current

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Two long straight wires P and Q carrying equal current 10A each were kept parallel to each other at 5 cm distance. Magnitude of magnetic force experienced by 10 cm length of wire P is

F_{1}

. If distance between wires is halved and currents on them are doubled, force

F_{2}

on 10 cm length of wire P will be :

(A) $8 F_{1}$ ✓ Correct
(B) $10 F_{1}$
(C) $F_{1} /8$
(D) $F_{1} /10$

Answer: (A)

Solution

The force per unit length between two parallel wires is

\frac{μ _{0} i _{1} i _{2}}{2 π d}

, growing with the product of the currents and shrinking with the separation. Doubling each current multiplies the product of currents by four, and halving the separation doubles the force once more, for a combined factor of

\frac{4}{1/2} = 8

. The new force on the same length of wire is

8 F_{1}

JEE Main · 2023 · 24 Jan 2023 · Shift 1 · Single correct option

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JEE Main · 2023 · 24 Jan 2023 · Shift 1 · Magnetic Effects of Current

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