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Question

The ends of a coil, having 20 turns, area of cross-section 1 cm2 and resistance 2 Ω, are connected to a galvanometer of resistance 40 Ω. The plane of coil is inclined at an angle 30∘ to the direction of a magnetic field of intensity 1.5 T. The coil is quickly pulled out of the field, to a region of zero magnetic field. Calculate the total charge that passes through the galvanometer, during this interval.

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Solution

The correct option is **A** 35.7 μC

Given,

N=20 turns

A=1 cm2=10−4 m2

R=2+40=42 Ω

B=1.5 T

θ=90∘−30∘=60∘

Total flux linked with the coil having turns N and area A is:

ϕ1=N(→B.→A)=NBAcosθ

Initial flux, ϕ1=NBAcos60∘

ϕ1=NBA2

When the coil is pulled out of the field, the flux becomes zero,

∴ Final flux, ϕ2=0

So, the change in flux is,

|Δϕ|=NBA2

The charge flowed through circuit is:

q=ΔϕR=NBA2R

⇒q=20×1.5×10−42×42

∴ q=0.357×10−4C=35.7 μC

Hence, option (A) is the correct answer.

Why this Question? Short Trick: To solve these type of questions, we can use the following expression for charge flown, q=ΔϕR |

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