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A conducting loop is made to rotate in a uniform magnetic field. When the loop rotates through an angle of $60^{o}$ , total charge flown through the loop

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depends upon average rate of change of flux linked with the loop

depends upon initial flux linked with the loop only

depends upon final flux linked with the loop only

depends upon the total change in magnetic flux linked with the loop

answer is D.

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Detailed Solution

If R be the resistance of the loop, induced current $i = \frac{1}{R} x ε = \frac{1}{R} x (- \frac{dϕ}{dt}) \Rightarrow idt = - \frac{dϕ}{R}$

$\Rightarrow Q = \int_{0}^{Q} dQ = - \int_{ϕ_{i}}^{ϕ_{f}} \frac{dϕ}{R} = \frac{ϕ_{i} - ϕ_{f}}{R} \Rightarrow Q \propto (ϕ_{i} - ϕ_{f})$

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