The magnetic force between wires as shown in figure is :- - Vidyadip

MCQ

The magnetic force between wires as shown in figure is :-

A
$\frac{{{\mu _0}i{I^2}}}{{2\pi }}\ln \left( {\frac{{x + l}}{{2x}}} \right)$
B
$\frac{{{\mu _0}i{I^2}}}{{2\pi }}\ln \left( {\frac{{2x + l}}{{2x}}} \right)$
✓
$\frac{{{\mu _0}i{I}}}{{2\pi }}\ln \left( {\frac{{x + l}}{x}} \right)$
D
None of these

✓

Answer

Correct option: C.

$\frac{{{\mu _0}i{I}}}{{2\pi }}\ln \left( {\frac{{x + l}}{x}} \right)$

c
Magnetic field at $\mathrm{dr}, \mathrm{B}=\frac{\mu_{0} \mathrm{I}}{2 \pi \mathrm{r}}$

Force on small element at a distance $r$ of wire of length $L$ is $d F=i(d r)\left(\frac{\mu_{0} I}{2 \pi r}\right)$

$\mathrm{F}=\frac{\mu_{0} \mathrm{i} \mathrm{I}}{2 \pi} \int_{\mathrm{x}}^{\mathrm{x}+\mathrm{L}} \frac{\mathrm{dr}}{\mathrm{r}}=\frac{\mu_{0} \mathrm{i} \mathrm{I}}{2 \pi} \ln \left(\frac{\mathrm{x}+\mathrm{L}}{\mathrm{x}}\right)$

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