Question

The magnetic force between wires as shown in figure is

• A. $\frac{\mu_{0} i I ^{2}}{2 \pi} \ell n \left(\frac{ x +\ell}{2 x }\right)$
• B. $\frac{\mu_{0} iI ^{2}}{2 \pi} \ell n \left(\frac{2 x +\ell}{2 x }\right)$
• C. $\frac{\mu_{0} iI }{2 \pi} \ln \left(\frac{ x +\ell}{ x }\right)$
• D. None of these

Answer 1

Answer: (C)

Magnetic field at $dr , B =\frac{\mu_{0} I }{2 \pi r }$
Force on small element at a distance $r$ of wire of length
1 is $dF = i ( dr )\left(\frac{\mu_{0} I }{2 \pi r }\right)$
$F =\frac{\mu_{0} i I }{2 \pi} \int\limits_{ x }^{ x +\ell} \frac{dr}{r}=\frac{\mu_{0} i I }{2 \pi} \ell n \left(\frac{ x +\ell}{ x }\right)$