Question

The magnetic flux through a circuit of resistance R changes by an amount Δϕ in a time Δt. Then the total quantity of electric charge Q that passes any point in the circuit during the time Δt is represented by

• A. $Q=\frac{1}{R}.\frac{Δ\phi}{Δt}$
• B. $Q=\frac{Δ\phi}{R}$
• C. $Q=\frac{Δ\phi}{Δt}$
• D. $Q=R.\frac{Δ\phi}{Δt}$

Hint:

When the magnetic flux linked with a circuit changes, an emf is induced in the circuit that stays as long as the flux keeps changing. 

Answer 1

The Correct Option is B

As, e = \(| {ΔΦ \over Δt} |\)

Current or I = e/R = ΔΦ​/RΔt

So, charge Q = IΔt

= ΔΦ​/RΔt . Δt

= ΔΦ/R

Therefore, option B is the correct answer.

Answer 2

Using the concept of Faraday’s law of EMI. By using this concept, we can find the total amount of charges passing through the circuit to get the required solution.

Formula used: \(e=\frac{Δϕ}{Δt}\)

Where,

• e is the induced voltage,
• ΔΦ is the change in magnetic flux 
• Δt is the change in time.

From Faraday’s law of EMI, the emf induced in the circuit is given as,

\(e=\frac{Δϕ}{Δt}\)

And if R is the resistance in the circuit then - 

\(I=\frac{e}{R}\)

\(⇒I=\frac{Δϕ}{Δt.R}\)

The total amount of charge that passes through the circuit becomes - 

\(∵Q=I×Δt\)

\(⇒Q=\frac{Δϕ}{Δt.R}.Δt\)

\(⇒Q=\frac{Δϕ}{R}\)

So, the total amount of charge passing through the circuit is given by \(\frac{Δϕ}{R}\).

The magnetic flux through a circuit of resistance R changes by an amount Δϕ in a time Δt. Then the total quantity of electric charge Q that passes any point in the circuit during the time Δt is represented by ΔΦ/R.

Hence, the correct option is B.

Note: When the magnetic flux linked with a circuit changes, an emf is induced in the circuit that stays as long as the flux keeps changing. The induced emf opposes the cause due to which it is produced.