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Question

A thin circular ring of the area Ais held perpendicular to a uniform magnetic field Bof induction. A small cut is made in the ring and a galvanometer is connected across the ends such that the total resistance of the circuit is R. When the ring is suddenly squeezed to zero areas, the charge flowing through the galvanometer is:


  1. BRA

  2. ABR

  3. ABR

  4. None

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Solution

The correct option is B

ABR


The explanation for the correct option:

Step 1: Given data

Area=A

Resistance=R

Magneticfield=B

Step 2: Formula

φ=BA

Step 3: Calculation

The magnetic flux is given by the formula

φ=BA

I=Qt----------(1)

The induced emf is given by:

E=φt

Here,

φ is the change in magnetic flux.

t is the change in time.

After the ring is suddenly squeezed to zero areas,

E=φt

φ=φ1-φ2whereφ1isinitial=0,φ2isfinal=φ

=φ-0t=φt----(2)

Induced emf is produced when the magnetic flux changes.

The current is given by
I=ER

Here,

I is the current.

t is time.

E is the emf.

Now substitute the value of current and induced emf in the above equation ( equating equation 1and 2)
Qt=BARt
Q=ABR

Hence, Option(B) is correct.


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