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Question

A coil of cross-sectional area A having n turns is placed in a uniform magnetic field B. When it is rotated with an angular velocity ω, the maximum e.m.f. induced in the coil will be


A

nBAω

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B

(3/2)nBAω

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C

3nBAω

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D

(1/2)nBAω

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Solution

The correct option is A

nBAω


Step 1: Given

Given, a coil with the area of cross-section A and n turn is given which is to be placed in a uniform magnetic field B. later coil is rotated with an angular velocity ω then the maximum e.m.f. ε0 induced in the coil is required.

Diagram representing the given condition-

Step 2: Calculate the magnetic flux ϕ

The magnetic flux linking to the coil, ϕ=nB.Aϕ=nBAcosθ

now, angular velocity ω=θtθ=ωt

here, θ is the angle of rotation of coil with time t.

then, ϕ=nBAcosωt

Step 3: Calculate the emf ε and Maximum emf ε0

therefore, the emf induced in the coil, ε=-dϕdtε=-dnBAcosωtdtε=-nBA-sinωtωε=nBAωsinωt

now, the emf will be maximum at sinωt=1

sinωt=1ωt=90°θ=90°

so, the maximum emf ,

ε0=nBAω.1ε0=nBAω

Thus, the maximum emf ε0 induced in the coil is nBAω.

Hence, option A is correct.


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