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 in the coil?
Practice Questions
1 question
Q1
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 in the coil?
50 V
100 V
200 V
400 V
Using Faraday's law, EMF = -N * (ΔB/Δt) = -100 * ((1.5 - 0.5) / 2) = -100 * (1 / 2) = -50 V. The magnitude is 50 V.
Questions & Step-by-step Solutions
1 item
Q
Q: 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 in the coil?
Solution: Using Faraday's law, EMF = -N * (ΔB/Δt) = -100 * ((1.5 - 0.5) / 2) = -100 * (1 / 2) = -50 V. The magnitude is 50 V.
Steps: 8
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: Use Faraday's law of electromagnetic induction to calculate the induced EMF: EMF = -N * (ΔB/Δt).
Step 6: Substitute the values into the formula: EMF = -100 * (1.0 T / 2 s).
Step 7: Simplify the calculation: EMF = -100 * 0.5 = -50 V.
Step 8: State the magnitude of the induced EMF, which is 50 V (ignoring the negative sign as it indicates direction).
