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NEET PHYSICSEasy

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 F⃗\vec{F}, the net force on the remaining three arms of the loop is

A

3\vec{F}

B

-\vec{F}

C

-3\vec{F}

D

\vec{F}

Step-by-Step Solution

  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 (∮dl⃗\oint d\vec{l}) for a closed loop is zero, and F⃗net=I(∮dl⃗)×B⃗=0\vec{F}_{net} = I(\oint d\vec{l}) \times \vec{B} = 0 .
  2. Application: For a square loop with four arms, the total force is the sum of the forces on individual arms: F⃗net=F⃗arm1+F⃗remaining=0\vec{F}_{net} = \vec{F}_{arm1} + \vec{F}_{remaining} = 0.
  3. Calculation: Given that the force on one arm is F⃗arm1=F⃗\vec{F}_{arm1} = \vec{F}, we can substitute this into the equilibrium equation: F⃗+F⃗remaining=0⇒F⃗remaining=−F⃗\vec{F} + \vec{F}_{remaining} = 0 \Rightarrow \vec{F}_{remaining} = -\vec{F}
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