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A uniform magnetic field of 0.3 T is established along the +ve Z direction. A rectangular loop of sides 10 cm and 5 cm carries a current of 12 A is placed as shown in figure. The torque acting on the loop is ______ Nm.

Asked in GSEB Board March 2023 · Torque and potential energy

• (1) -1.8×10⁻² ̂j
• (2) -1.8×10⁻² ̂i
• (3) 1.8×10⁻² ̂i
• (4) Zero

Step-by-step solution

Why the other options are wrong

• (1) The torque for a loop standing in the YZ plane, where ⃗m lies along ̂i: then ⃗m×⃗B=0.06 ̂i×0.3 ̂k, which is -1.8×10⁻² ̂j. The loop in the figure lies flat in the XY plane instead.
• (2) The torque for a loop standing in the XZ plane with ⃗m along -̂j. Same size mB, but it again needs the plane of the loop to contain the Z axis.
• (3) The full mB=0.06×0.3, taken as though ⃗m were perpendicular to ⃗B. This is the usual slip of reading 'the loop lies in the XY plane' as 'the loop is perpendicular to ⃗B': the loop's plane is perpendicular to ⃗m, not to ⃗B.

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