A coil with 100 turns is placed in a magnetic field that changes from 0.2 T to 0
Practice Questions
Q1
A coil with 100 turns is placed in a magnetic field that changes from 0.2 T to 0.5 T in 2 seconds. What is the induced EMF?
15 V
30 V
5 V
10 V
Questions & Step-by-Step Solutions
A coil with 100 turns is placed in a magnetic field that changes from 0.2 T to 0.5 T in 2 seconds. What is the induced EMF?
Step 1: Identify the number of turns in the coil, which is given as 100 turns (N = 100).
Step 2: Determine the initial magnetic field (B_initial) and the final magnetic field (B_final). Here, B_initial = 0.2 T and B_final = 0.5 T.
Step 3: Calculate the change in magnetic field (dB) by subtracting B_initial from B_final: dB = B_final - B_initial = 0.5 T - 0.2 T = 0.3 T.
Step 4: Identify the time duration (dt) over which the change occurs, which is given as 2 seconds.
Step 5: Calculate the rate of change of the magnetic field (dB/dt) by dividing the change in magnetic field (dB) by the time duration (dt): dB/dt = dB / dt = 0.3 T / 2 s = 0.15 T/s.
Step 6: Use the formula for induced EMF (ε): ε = -N(dB/dt). Substitute the values: ε = -100 * 0.15 T/s.
Step 7: Calculate the induced EMF: ε = -15 V.
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 the change in magnetic field strength over time affects the induced EMF.
Negative Sign in Induced EMF – The negative sign indicates the direction of the induced EMF according to Lenz's Law, which states that the induced EMF will oppose the change in magnetic flux.
