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A wire carrying current I is tied between points P and Q and is in the shape of a circular arch of radius R due to a uniform magnetic field B (perpendicular to the plane of the paper, shown by ×××) in the vicinity of the wire. If the wire subtends an angle 2θ₀ at the centre of the circle (of which it forms an arch) then the tension in the wire is

Asked in JEE Main Online 2015 · Force on a wire in a field

• (1) IBR
• (2) (IBR)/(sin θ₀)
• (3) (IBR)/(2 sin θ₀)
• (4) (IBRθ₀)/(sin θ₀)

Step-by-step solution

Why the other options are wrong

• (2) Balances the whole arc's force against the tension components as if the tension were fixed by the end angle.
• (3) Balances the whole arc's force 2IBR sin θ₀ against only one end's tension component.
• (4) Uses the arc length 2Rθ₀ instead of the chord in the force balance.

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