First slide

Magnetic flux and induced emf

Question

A uniforrn magnetic field B = 0.5 T exists in a circular region of radius R=5m.A loop of radius R = 5 m encloses the magnetic field at t = 0 and then pulled at uniform speed v = 2 m/s in the plane of the paper. The induced emf in the loop at time t = 3 sec (in V) is _________

Moderate

Solution

$\begin{array}{l} O_{1} M = (v t - R) + (\frac{2 R - v t}{2}) = \frac{v t}{2} \\ P M = \sqrt{R^{2} - {(O_{1} M)}^{2}} = \sqrt{R^{2} - {(\frac{v t}{2})}^{2}} = \frac{\sqrt{4 R^{2} - V^{2} t^{2}}}{2} \\ P N = 2 P M = l = \sqrt{4 R^{2} - V^{2} t^{2}} \\ ∴ E = B V l \\ = B V \sqrt{4 R^{2} - V^{2} t^{2}}, given R = 5 m, v = 2 m / s, t = 3 \sec \\ = 0.5 \times 2 \sqrt{4 \times 25 - 4 \times 9} = 8 V \end{array}$

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