    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.

A
35.7 μC
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B
357 μC
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C
3.57 μC
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D
375 μC
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Solution

## The correct option is A 35.7 μCGiven, 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  Suggest Corrections  0      Explore more