​Consider two coils A and B. Suppose coil A is replaced with coil B that has the number of loops 2 times as that of loop A and the rate of change of magnetic flux is constant. Determine the ratio of the initial to the final induced EMF.​

Correct option is C

Correct Answer: C 1 : 2

Explanation:
The induced electromotive force (EMF) in a coil is given by Faraday's Law of Electromagnetic Induction:

​$$EMF=− -N \frac{d\Phi}{dt}$$​​

Where:

• N is the number of loops in the coil.
• $$\frac{d\Phi}{dt}$$​ is the rate of change of magnetic flux, which is constant in this case.

Initially, the EMF for coil A is proportional to the number of loops in coil A:

​$$\text{EMF}_{\text{initial}} = N_A \frac{d\Phi}{dt}$$​​

When coil A is replaced with coil B, which has twice the number of loops as coil A (NB = 2$$N_A$$​​), the EMF becomes:

​$$\text{EMF}_{\text{final}} = N_B \frac{d\Phi}{dt} = 2N_A \frac{d\Phi}{dt}$$​​

The ratio of the initial to the final EMF is:

Thus, the ratio of the initial to the final EMF is 1 : 2.

Information Booster:

·         Faraday's Law states that the EMF induced in a coil is directly proportional to the number of loops and the rate of change of magnetic flux.

·         Increasing the number of loops increases the EMF proportionally.

·         Magnetic flux (Φ\PhiΦ) depends on the magnetic field strength and the area of the coil through which the field passes.

·         The negative sign in Faraday's Law signifies Lenz's Law, which states that the induced EMF opposes the change causing it.

·         Coils with more loops are more efficient in applications requiring high EMF, such as transformers and generators.