Two long and parallel straight wires, each carrying current 'I' in the same direction, are separated by a distance of 40 cm. If the force of attraction per metre between them, is \( 2 \times 10^{-6}\,\mathrm{N/m} \), the value of 'I' will be: (Given: \( \mu_0 = 4\pi \times 10^{-7}\,\mathrm{T\,m\,A^{-1}} \))
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 2 A
The force per unit length between two long parallel currents is
\( \displaystyle \frac{F}{L} = \frac{\mu_0 I_1 I_2}{2\pi d} \)
Here \( I_1 = I_2 = I \) and \( d = 40\,\mathrm{cm} = 0.4\,\mathrm{m} \).
\( \displaystyle I^{2} = \frac{2\pi d}{\mu_0}\cdot\frac{F}{L} = \frac{2\pi \times 0.4 \times 2\times10^{-6}}{4\pi\times10^{-7}} = 4 \)
\( \displaystyle I = 2\,\mathrm{A} \)