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Faraday's Law Of Induction - Practice Questions & MCQ

Edited By admin | Updated on Sep 25, 2023 25:23 PM | #NEET

Quick Facts

  • Faraday's law of induction is considered one the most difficult concept.

  • 44 Questions around this concept.

Solve by difficulty

Figure shows three regions of magnetic field, each of area A, and in each region magnitude of magnetic field decreases at a constant rate a. If  \vec{E}is induced electric field then value of line integral \oint \vec{E}.d \vec{r} along the given loop is equal to

 A small circular loop of wire of radius a is located at the centre of a much larger circular wire loop of radius b.  The two loops are in the same plane.  The outer loop of radius b carries an alternating current I=Io cos (ωt).  The emf induced in the smaller inner loop is nearly :

 

In the figure shown a square loop PQRS of side 'a' and resistance 'r' is placed near an infinitely long wire carrying a constant current I. The sides PQ and RS are parallel to the wire. The wire and the loop are in the same plane. The loop is rotated by 180º about an axis parallel to the long wire and passing through the mid points of the side QR and PS. The total amount of charge which passes through any point of the loop during rotation is  :

 A coil of resistance 400\Omega is placed in a magnetic field. If the magnetic flux \phi (wb) linked with the coil varies with time t (\sec) as \phi=50t^{2}+4 . The current in the coil at t=2 sec is:

 

The current (I) in the inductance is varying with time according to the plot shown in figure.

 

Which one of the following is the correct variation of voltage with time in the coil?

An electron moves on a straight line path XY as shown. The abcd is a coil adjacent to the path of electron What will be the direction of current if any, induced in the coil?

 

Concepts Covered - 1

Faraday's law of induction

 Faraday’s First Law-

Whenever the number of magnetic lines of force (Magnetic Flux) passing through a circuit changes an emf called induced emf is produced in the circuit. The induced emf persists only as long as there is a change of flux.

Faraday’s Second Law-

The induced emf is given by the rate of change of magnetic flux linked with the circuit.

i.e  Rate of change of magnetic Flux= \varepsilon = \frac{-d\phi }{dt}

where d\phi\rightarrow \phi _{2}-\phi _{1}= change in flux

And For N turns it is given as   \varepsilon = \frac{-Nd\phi }{dt} where N= Number of turns in the Coil .

The negative sign indicates that induced emf (e) opposes the change of flux.
 And this Flux may change with time in several ways

I.e As \phi = BA\cos \Theta  So  \varepsilon = N\frac{-d}{dt}(BA\cos \Theta )

1.If Area (A) change then \varepsilon = -NB\cos \Theta \left ( \frac{dA}{dt} \right )

2.If Magnetic field (B) change then \varepsilon = -NA\cos \Theta \left ( \frac{dB}{dt} \right )

3. If Angle (θ ) change then  \varepsilon = -NAB\frac{d\left ( \cos \Theta \right )}{d\Theta }\times \frac{d\Theta }{dt}   or  \varepsilon =+NBA\; \omega \sin \Theta

  • Induced Current-

         I= \frac{\varepsilon }{R}=\frac{-N}{R}\frac{d\phi }{dt}

      where 

R\rightarrow Resistance

\frac{d\phi }{dt}\rightarrow Rate of change of flux

  • Induced Charge-

    dq= i.dt= \frac{-N}{R}\frac{d\phi }{dt}.dt

    dq= \frac{-N}{R}d\phi

 I.e Induced Charge time-independent.

  • Induced Power-

         P= \frac{\varepsilon ^{2}}{R}= \frac{N^{2}}{R}\left ( \frac{d\phi }{dt} \right )^{2}

      i.e - Induced Power depends on both time and resistance

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Faraday's law of induction

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