A square loop carrying a current , is placed near and coplanar with a long straight conductor carrying a current , the net force on the loop will be [2016]

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Q.
A square loop $A B C D$ carrying a current $i$ , is placed near and coplanar with a long straight conductor $X Y$ carrying a current $I$ , the net force on the loop will be [2016]

1 $\frac{2 μ_{0} I i L}{3 π}$

2 $\frac{μ_{0} I i L}{2 π}$

3 $\frac{2 μ_{0} I i}{3 π}$

4 $\frac{μ_{0} I i}{2 π}$

Ans.
(3)

Force on arm $A B$ due to current in conductor $X Y$ is

   $F_{1} = \frac{μ_{0}}{4 π} \frac{2 I i L}{(L / 2)} = \frac{μ_{0} I i}{π}$

acting towards $X Y$ in the plane of the loop.

Force on arm $C D$ due to current in conductor $X Y$ is

   $F_{2} = \frac{μ_{0}}{4 π} \frac{2 I i L}{3 (L / 2)} = \frac{μ_{0} I i}{3 π}$

acting away from $X Y$ in the plane of the loop.

$∴$    $Net force on the loop = F_{1} - F_{2} = \frac{μ_{0} I i}{π} [1 - \frac{1}{3}] = \frac{2 μ_{0} I i}{3 π}$

Solution

Q.
A square loop $A B C D$ carrying a current $i$ , is placed near and coplanar with a long straight conductor $X Y$ carrying a current $I$ , the net force on the loop will be [2016]

1 $\frac{2 μ_{0} I i L}{3 π}$

2 $\frac{μ_{0} I i L}{2 π}$

3 $\frac{2 μ_{0} I i}{3 π}$

4 $\frac{μ_{0} I i}{2 π}$

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Solution

Q. 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 [2016]

1 2μ0IiL3π

2 μ0IiL2π

3 2μ0Ii3π

4 μ0Ii2π

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Q.
A square loop $A B C D$ carrying a current $i$ , is placed near and coplanar with a long straight conductor $X Y$ carrying a current $I$ , the net force on the loop will be [2016]

1 $\frac{2 μ_{0} I i L}{3 π}$

2 $\frac{μ_{0} I i L}{2 π}$

3 $\frac{2 μ_{0} I i}{3 π}$

4 $\frac{μ_{0} I i}{2 π}$