If a magnetic field is increasing at a rate of 0.1 T/s, what is the induced EMF

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Question: If a magnetic field is increasing at a rate of 0.1 T/s, what is the induced EMF in a coil of 50 turns and area 0.2 m²? (2021)

Options:

Correct Answer: 1 V

Exam Year: 2021

Solution:

Induced EMF (ε) = -N * (dB/dt) * A = -50 * 0.1 T/s * 0.2 m² = -1 V.

If a magnetic field is increasing at a rate of 0.1 T/s, what is the induced EMF in a coil of 50 turns and area 0.2 m²? (2021)

If a magnetic field is increasing at a rate of 0.1 T/s, what is the induced EMF in a coil of 50 turns and area 0.2 m²? (2021)

Step 1: Identify the given values from the problem. We have the rate of change of the magnetic field (dB/dt) as 0.1 T/s, the number of turns (N) in the coil as 50, and the area (A) of the coil as 0.2 m².
Step 2: Write down the formula for induced EMF (ε). The formula is ε = -N * (dB/dt) * A.
Step 3: Substitute the values into the formula. Replace N with 50, dB/dt with 0.1 T/s, and A with 0.2 m².
Step 4: Calculate the induced EMF. Multiply 50 (turns) by 0.1 (T/s) and then by 0.2 (m²).
Step 5: Perform the multiplication: 50 * 0.1 = 5, then 5 * 0.2 = 1.
Step 6: Since the formula includes a negative sign, the final answer for the induced EMF is -1 V.

Faraday's Law of Electromagnetic Induction – This law states that the induced electromotive force (EMF) in a closed loop is proportional to the rate of change of the magnetic flux through the loop.
Induced EMF Calculation – The formula for calculating induced EMF involves the number of turns in the coil, the rate of change of the magnetic field, and the area of the coil.