Two long and parallel straight wires A and B carrying currents of 10.0 A and 5.0 A in the same direction are separated by a distance of 5.0 cm. Estimate the force on a 10 cm section of wire A.
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → $2 × 10^{-5} N$
Given:
$I_1 = 10\,A$
$I_2 = 5\,A$
$r = 5.0\,cm = 0.05\,m$
$l = 10\,cm = 0.1\,m$
Magnetic field due to wire B at distance r:
$B = \frac{\mu_0 I_2}{2 \pi r}$
$B = \frac{4\pi \times 10^{-7} \times 5}{2 \pi \times 0.05}$
$B = \frac{2 \times 10^{-7} \times 5}{0.05}$
$B = 2 \times 10^{-5}\,T$
Force on wire A:
$F = I_1 l B$
$F = 10 \times 0.1 \times 2 \times 10^{-5}$
$F = 2 \times 10^{-5}\,N$
Since currents are in the same direction, force is attractive
.Final Answer: Force on 10 cm section of wire A = $2 × 10^{-5} N$ (attractive).