Two long parallel wires separated by a distance of 2.50 cm repel each other with a force of \( 4\times10^{-5}\,\mathrm{N/m} \). The current in one wire is 0.5 A. The current in the second wire will be
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 10 A
The force per unit length between two long parallel wires is
\( \displaystyle \frac{F}{L} = \frac{\mu_0 I_1 I_2}{2\pi d} \)
(The wires repel, so the currents are in opposite directions; the magnitude does not depend on this.)
\( d = 2.50\,\mathrm{cm} = 2.5\times10^{-2}\,\mathrm{m} \)
\( \mu_0/2\pi = 2\times10^{-7}\,\mathrm{T\,m\,A^{-1}} \)
\( I_1 = 0.5\,\mathrm{A} \)
\( \displaystyle 4\times10^{-5} = \frac{2\times10^{-7} \times 0.5 \times I_2}{2.5\times10^{-2}} = 4\times10^{-6}\,I_2 \)
\( \displaystyle I_2 = \frac{4\times10^{-5}}{4\times10^{-6}} = 10\,\mathrm{A} \)