A closed loop PQRS carries current in a uniform magnetic field. The forces on sides PS, SR and RQ are F₁, F₂ and F₃ along the directions shown in the diagram. Find the magnitude of the force on side QP. [Image]
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Question

A closed loop PQRS carries current in a uniform magnetic field. The forces on sides PS, SR and RQ are F₁, F₂ and F₃ along the directions shown in the diagram. Find the magnitude of the force on side QP. [Image]

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G1 Physics · Accepted Answer

Step 1: For any complete closed loop in a UNIFORM magnetic field, total magnetic force is zero: F⃗_PS+F⃗_SR+F⃗_RQ+F⃗_QP=0. Step 2: In the figure, F⃗_PS is leftward with magnitude F₁, F⃗_SR is downward with magnitude F₂, and F⃗_RQ is rightward with magnitude F₃. Step 3: Therefore F⃗_QP has x-component F₁−F₃ and y-component F₂ to balance the other forces. Step 4: |F⃗_QP| = √[(F₃−F₁)²+F₂²]. Final answer: (B) √[(F₃ − F₁)² + F₂²].