A closed coil having $$20$$ turns, area of $$cross-section$$ $$1$$ $$cm2$$ and negligible resistance are connected to a ballistic galvanometer of resistance $$30$$ ohms. If the normal of the coil is inclined at $$60o$$ to the direction of a magnetic field of intensity $$1.5$$ $$Wb/m2$$, the coil is quickly pulled out of the field to a region of zero magnetic field, the charge (in$$ μ$$C) passed through the galvanometer is $$______$$.

Question

A closed coil having $$20$$ turns, area of $$cross-section$$ $$1$$ $$cm2$$ and  negligible resistance are connected to a ballistic galvanometer of resistance $$30$$ ohms. If the normal of the coil is inclined at $$60o$$ to the direction of a magnetic field of intensity $$1.5$$ $$Wb/m2$$, the coil is quickly pulled out of the field to a region of zero magnetic field, the charge (in$$ μ$$C) passed through the galvanometer is $$______$$.

Infinity Learn · Accepted Answer

The total flux linked with the coil having turns N and area A is

$ϕ_{initial} = N (\vec{B} \cdot \vec{A}) = N B A \cos θ = N B A \cos 60^{\circ} = \frac{N B A}{2}$

When the coil is pulled out, the flux becomes zero $ϕ_{final} = 0$

$The change in flux is Δ ϕ = \frac{N B A}{2} - 0$

Hence the charge flowed through the circuit is

$q = \frac{Δ ϕ}{R} = \frac{N B A}{2 R} = \frac{20 \times 1.5 \times 10^{- 4}}{2 \times 30} = 5.0 \times 10^{- 5} C = 50.0 μ C$

Magnetic flux and induced emf

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