# A square loop ABCD carrying a current i, is placed near and coplanar with a long straight conductor XY carrying a current I, the net force on the loop will be: Option 1) Option 2) Option 3) Option 4)

Force between two parallel current carrying conductors -

$F=\frac{\mu }{4\pi } \frac{2I_{1 I_{2}}}{a} l$

$\frac{F}{l}=\frac{\mu o}{4\pi } \frac{2I_{1 I_{2}}}{a}$

- wherein

I1 and I2 current carrying two parallel wires

a-seperation between two wires

force on $F_{1}= \frac{\mu _{0}}{4\pi }\frac{2Iil}{\frac{l}{2}} = \frac{\mu _{0} Ii}{3\pi }$

force  $f_{2 }= \frac{\mu _{0}}{4\pi }\frac{2IiL}{3\left ( \frac{L}{2} \right )} = \frac{\mu_{0} }{3\pi }$

Net force on the loop

$f_{1}-f_{2} = \frac{\mu _{0Ii}}{\pi }\left [ 1-\frac{1}{3} \right ]$

$= \frac{2 \mu _{0}Ii}{3\pi }$

Option 1)

This option is correct.

Option 2)

This option is incorrect.

Option 3)

This option is incorrect.

Option 4)

This option is incorrect.

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