The area and the number of turns in a loop of wire are doubled. Assuming that all the other parameters remain the same, what happens to the induced emf in that loop of wire? a. It is reduced by a factor of 4. b. It is doubled. c. It is reduced by a factor of 2. d. It is quadrupled. e. It stays the same.
The correct answer and explanation is:
The correct answer is d. It is quadrupled.
Explanation:
The induced electromotive force (emf) in a loop of wire is given by Faraday’s Law of Induction, which states that the induced emf is equal to the rate of change of magnetic flux through the loop. Mathematically, this is represented as: ϵ=−NdΦBdt\epsilon = -N \frac{d\Phi_B}{dt}
Where:
- ϵ\epsilon is the induced emf,
- NN is the number of turns in the coil,
- ΦB\Phi_B is the magnetic flux, and
- dΦBdt\frac{d\Phi_B}{dt} is the rate of change of the magnetic flux.
The magnetic flux ΦB\Phi_B is given by: ΦB=B⋅A\Phi_B = B \cdot A
Where:
- BB is the magnetic field strength,
- AA is the area of the loop.
If the area AA of the loop is doubled, the magnetic flux ΦB\Phi_B also doubles because flux is directly proportional to area. Similarly, if the number of turns NN in the loop is doubled, the total induced emf will also be doubled because the emf is directly proportional to the number of turns. Therefore, doubling both the area and the number of turns results in the emf being: New emf=2×2×Original emf=4×Original emf\text{New emf} = 2 \times 2 \times \text{Original emf} = 4 \times \text{Original emf}
This means the induced emf increases by a factor of 4, so the correct answer is d. It is quadrupled.