First slide

Force on a current carrying wire placed in a magnetic field

Question

A current carry square loop ABCD is placed at a distance a from an infinitely long current carrying long straight conductor PQ as shown in the figure. The conductor PQ lies in the plane of the loop. Then

Moderate

A

magnetic potential energy stored in the system is zero.
B

the square loop experiences a net torque.
C

the loop experiences a net force towards the conductor PQ.
D

the loop experiences a net force away from PQ.

Solution

$\begin{array}{l} |{\vec{F}}_{DA}| = |{\vec{F}}_{BC}| \\ {\vec{F}}_{AB} = i \vec{AB} \times {\vec{B}}_{1} \\ F_{AB} = i \times a \times \frac{μ_{o} I}{2 πa} \\ {\vec{F}}_{CD} = i \vec{CD} \times {\vec{B}}_{2} = i \times a \times \frac{μ_{o} I}{2 π (2 a)} \\ ∴ F_{A B} > F_{CD} \end{array}$

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