Question

A closed coil of area A, number of turns Nis placed in a field B. Then an alternating emf can be obtainer
,
1) By continuously increasing A
2) By continuously increasing N
3) By continuously increasing B
4) By rotating the coil continuosly in the field.​

Answer 1

Answer

option 4 is correct

Explanation:

Answer 2

Answer:

An alternating EMF can be obtained by a closed coil of area A, number of turns N that is placed in a magnetic field B by Rotating the coil continuously in the field.

Explanation:

Faraday's Law of Induction:

This law states that "an electromotive force is induced by a change in the magnetic flux".

Magnetic Flux:

It is the magnetic field passing through a given surface. It is usually denoted by Φ. Lets consider the magnetic field to be B and it is passing through a surface of area A, then

                                        Φ=BA

Induced EMF:

According to Faraday's Law of Induction, the induced EMF ε is given by

                                      ε=-dΦ/dt

• Step 1: The closed coil has an area A and N number of turns.   Therefore,

              Φ=NBA

• Step 2: The induced EMF is given by

                      ε=-dΦ/dt=-d(NBA)/dt

• Step 3: As per the question we require an alternating EMF, for that the rate of change of induced EMF should not be zero.

• Step 4: The first three options are describing a continuous increase, the implies the rate of change of that quantity is a constant. If that's the case then the Induced EMF will also be a constant and hence the rate of change of the same will be zero.
• Step 5: We will look into the last option which is rotating the coil continuously in the field. Whenever an object is rotating in a magnetic field the flux changes because the field lines passing through a specific area change.
• Step 6: Let us consider the speed of rotation to be ω radians/s. Therefore the area in terms angular displacement is given by              

                                          $A=R\theta$

        Rate of change of A,

                                          $\frac{dA}{dt}=R\frac{d\theta}{dt}$

•    Step 7: Putting the above result in the equation for induced EMF we get,  

                                           $\epsilon=\frac{d\phi}{dt}=NB\frac{dA}{dt}\\\\\epsilon=NBR\frac{d\theta}{dt}\\\epsilon=NBR\omega$

• Step 8: In the above equation, by continuously changing the angular velocity that is, by continuously rotating the coil the induced EMF can be changed continuously which implies an alternating EMF.

Therefore, the 4th option that is by rotating the coil continuously in a magnetic field an induced alternating EMF can be obtained