# A flat coil, $C$ of $n$ turn, area $A$ and resistance $R$, is placed in a uniform magnetic field of magnitude $B$. The plane of the coil is initially perpendicular to $B$. The coil is rotated by an angle $θ$ about a diameter and charge of amount $Q$ flows through it. Choose the correct alternatives.

This question has multiple correct options

**A**

## $θ=90_{o},Q=(BAn/R)$

**B**

## $θ=180_{o},Q=(2BAn/R)$

**C**

## $θ=180_{o},Q=0$

**D**

## $θ=360_{o},Q=0$

Hard

Solution

Verified by GMS

Correct options are A) , B) and D)

## Current through a coil rotating with angular velocity $ω$ is given by:

$i=RnBAωsinωt $

Charge flown on rotating the coil through an angle $θ$ is given by:

$Q=∫idt=∫ωi d(ωt)=∫ωi dθ$

$Q=R−nBAcosθ +RnBA $

For $θ=90_{0}$, $Q=R−nBAcos90_{0} +RnBA =0+RnBA =RnBA $

For $θ=180_{0}$, $Q=R−nBAcos180_{0} +RnBA =RnBA +RnBA =R2nBA $

For $θ=360_{0}$, $Q=R−nBAcos360_{0} +RnBA =R−nBA +RnBA =0$

For $θ=90_{0}$, $Q=R−nBAcos90_{0} +RnBA =0+RnBA =RnBA $

For $θ=180_{0}$, $Q=R−nBAcos180_{0} +RnBA =RnBA +RnBA =R2nBA $

For $θ=360_{0}$, $Q=R−nBAcos360_{0} +RnBA =R−nBA +RnBA =0$

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