A conducting wire bent in the shape of semicircle has length L and moves in its plane with constant velocity v. A uniform magnetic field B exists in the direction perpendicular to the plane of the wire. The velocity makes an angle 45 ° to the diameter joining free ends and the emf induced between the ends of the wire is Φ = α ( B v L ) . The value of constant α is

Question

A conducting wire bent in the shape of semicircle has length L and moves in its plane with constant velocity v. A uniform magnetic field B exists in the direction perpendicular to the plane of the wire. The velocity makes an angle 45 ° to the diameter joining free ends and the emf induced between the ends of the wire is Φ = α ( B v L ) . The value of constant α is, 2, 2 π, 1 2, 2 π

MARKS App · Accepted Answer

The induced emf in the semicircular wire is e = B l V sin θ For semicircular section the effective length is l = 2 r = 2 L π ∴ e = B × 2 L π × V × sin 45 = 2 π × B V L After comparing from given equation α = 2 π

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