A square current carrying loop is suspended in a uniform magnetic field acting in the plane of the loop. If th

Question

A square current carrying loop is suspended in a uniform magnetic field acting in the plane of the loop. If the force on one arm of the loop is $\vec{F}$, the net force on the remaining three arms of the loop is

Accepted Answer

1. **Net Force Principle:** The net magnetic force on any closed current-carrying loop placed in a uniform magnetic field is zero. This is because the vector sum of the displacement vectors ($\oint d\vec{l}$) for a closed loop is zero, and $\vec{F}_{net} = I(\oint d\vec{l}) 	imes \vec{B} = 0$ .
2. **Application:** For a square loop with four arms, the total force is the sum of the forces on individual arms: $\vec{F}_{net} = \vec{F}_{arm1} + \vec{F}_{remaining} = 0$.
3. **Calculation:** Given that the force on one arm is $\vec{F}_{arm1} = \vec{F}$, we can substitute this into the equilibrium equation:
   $$\vec{F} + \vec{F}_{remaining} = 0 \Rightarrow \vec{F}_{remaining} = -\vec{F}$$

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