Two long and parallel straight conducting wires carrying currents of 5 A and 10 A in same direction are separated by a distance of 2 cm. The force per unit length on one wire due to other is \( (\mu_0: 4\pi\times10^{-7}\,\mathrm{N\,A^{-2}}) \)
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( 5\times10^{-4}\,\mathrm{N/m} \); attractive force
The force per unit length between two long parallel current-carrying wires follows from the magnetic field of one wire acting on the current of the other: \( \frac{F}{L} = \frac{\mu_0I_1I_2}{2\pi d} \). Currents in the same direction attract each other and currents in opposite directions repel.
\( d = 2\,\mathrm{cm} = 0.02\,\mathrm{m} \)
\( \displaystyle \frac{F}{L} = \frac{(4\pi\times10^{-7})(5)(10)}{2\pi\times0.02}\,\mathrm{N\,m^{-1}} = 5\times10^{-4}\,\mathrm{N\,m^{-1}} \)
The currents are in the same direction, so the force is attractive.