A coil with 100 turns is placed in a magnetic field that changes from 0.5 T to 1

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Question: A coil with 100 turns is placed in a magnetic field that changes from 0.5 T to 1.5 T in 2 seconds. What is the induced EMF?

Options:

Correct Answer: 100 V

Solution:

Induced EMF = -N * (ΔB/Δt) = -100 * ((1.5 - 0.5)/2) = -100 * (1/2) = -50 V. The magnitude is 50 V.

A coil with 100 turns is placed in a magnetic field that changes from 0.5 T to 1.5 T in 2 seconds. What is the induced EMF?

A coil with 100 turns is placed in a magnetic field that changes from 0.5 T to 1.5 T in 2 seconds. What is the induced EMF?

Step 1: Identify the number of turns in the coil, which is 100 turns (N = 100).
Step 2: Determine the initial magnetic field (B_initial = 0.5 T) and the final magnetic field (B_final = 1.5 T).
Step 3: Calculate the change in magnetic field (ΔB) by subtracting the initial field from the final field: ΔB = B_final - B_initial = 1.5 T - 0.5 T = 1.0 T.
Step 4: Identify the time interval (Δt) over which the change occurs, which is 2 seconds.
Step 5: Calculate the rate of change of the magnetic field (ΔB/Δt) by dividing the change in magnetic field by the time interval: ΔB/Δt = 1.0 T / 2 s = 0.5 T/s.
Step 6: Use the formula for induced EMF: Induced EMF = -N * (ΔB/Δt). Substitute the values: Induced EMF = -100 * 0.5 T/s.
Step 7: Calculate the induced EMF: Induced EMF = -50 V.
Step 8: State the magnitude of the induced EMF, which is 50 V (ignoring the negative sign as it indicates direction).

Faraday's Law of Electromagnetic Induction – This law states that the induced EMF in a coil is proportional to the rate of change of magnetic flux through the coil.
Magnetic Flux Change – Understanding how changes in magnetic field strength over time affect the induced EMF in a coil.
Negative Sign in Induced EMF – The negative sign indicates the direction of the induced EMF according to Lenz's Law, but the magnitude is what is typically reported.