What is the induced EMF in a loop of wire when the magnetic field through it cha

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Question: What is the induced EMF in a loop of wire when the magnetic field through it changes at a rate of dB/dt?

Options:

Correct Answer: -dB/dt

Solution:

According to Faraday\'s law of electromagnetic induction, the induced EMF is given by ε = -dΦ/dt, where Φ is the magnetic flux.

What is the induced EMF in a loop of wire when the magnetic field through it changes at a rate of dB/dt?

What is the induced EMF in a loop of wire when the magnetic field through it changes at a rate of dB/dt?

Step 1: Understand that EMF stands for electromotive force, which is the voltage generated by a changing magnetic field.
Step 2: Recall Faraday's law of electromagnetic induction, which states that the induced EMF (ε) in a loop is related to the rate of change of magnetic flux (Φ) through the loop.
Step 3: Know that magnetic flux (Φ) is calculated as the product of the magnetic field (B) and the area (A) of the loop, and it can change if either B or A changes.
Step 4: The formula for induced EMF is ε = -dΦ/dt, where dΦ/dt is the rate of change of magnetic flux over time.
Step 5: If the magnetic field (B) changes at a rate of dB/dt, then the change in magnetic flux (dΦ) can be expressed in terms of dB/dt, considering the area of the loop is constant.
Step 6: Substitute the expression for dΦ into the EMF formula to find the induced EMF in terms of dB/dt.

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