JEE Main · 2022 · 26 Jun 2022 · Shift 2 · Magnetic Effects of Current

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Two 10 cm long, straight wires, each carrying a current of 5A are kept parallel to each other. If each wire experienced a force of

1 0^{- 5}

N, then separation between the wires is ______ cm.

Answer: 5

Solution

The force per unit length between two parallel current-carrying wires is:

\frac{F}{l} = \frac{μ _{0} I _{1} I _{2}}{2 π d}

For a 10 cm length:

F = \frac{μ _{0} I _{1} I _{2}}{2 π d} \times l

Given:

I_{1} = I_{2} = 5

F = 1 0^{- 5}

l = 0.1

μ_{0} = 4 π \times 1 0^{- 7}

T·m/A

1 0^{- 5} = \frac{2 \times 1 0 ^{- 7} \times 5 \times 5}{d} \times 0.1

1 0^{- 5} = \frac{50 \times 1 0 ^{- 7} \times 0.1}{d}

d = \frac{50 \times 1 0 ^{- 8}}{1 0 ^{- 5}} = 50 \times 1 0^{- 3} m = 5 cm

JEE Main · 2022 · 26 Jun 2022 · Shift 2 · Integer answer

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