Steps for Calculating Faraday's Law of
Electromagnetic Induction
Faraday's Law of Electromagnetic Induction states that a change in magnetic flux through a
circuit induces an electromotive force (EMF). The induced EMF is proportional to the rate of
change of magnetic flux. Here are the steps to follow when calculating problems related to
Faraday's Law.
Steps for Calculating Faraday's Law Problems:
1. Understand the Problem and Identify the Given Values
Identify the components of the problem: - Number of turns (N): The number of coils or
loops in the circuit.
- Change in magnetic flux (ΔΦ): The difference between the initial and final magnetic flux.
- Time interval (Δt): The time over which the change in magnetic flux occurs.
2. Calculate the Change in Magnetic Flux (ΔΦ)
The change in magnetic flux ΔΦ is calculated as:
ΔΦ = Φ(final) - Φ(initial)
Where:
• Φ(final) = B(final) A cos(θ)
• Φ(initial) = B(initial) A cos(θ)
3. Calculate the Rate of Change of Magnetic Flux
Once you've calculated ΔΦ, calculate the rate of change of magnetic flux:
dΦ/dt = ΔΦ / Δt
This represents the rate at which the magnetic flux changes over time.
4. Apply Faraday’s Law
Now, apply Faraday’s Law of Induction, which states:
EMF = -N (dΦ/dt)
Where:
- EMF is the induced electromotive force (voltage).
- N is the number of turns (coils) in the wire or loop.
- (dΦ/dt) is the rate of change of magnetic flux.
The negative sign indicates the direction of the induced EMF (Lenz’s Law).
5. Final Calculations
Once you have all the variables, plug them into the formula to calculate the induced EMF.
Units:
- EMF will be in volts (V).
- (dΦ/dt) will be in Weber per second (Wb/s), which is the same as Volts.
Example Problem Walkthrough:
Problem:
A coil with 150 turns has an area of 0.03 m². The magnetic field changes from 0.2 T to 0.5 T
in 0.4 s. Find the induced EMF.
Step-by-Step Solution:
1. Identify the given values:
• Number of turns N = 150
• Area A = 0.03 m²
• Initial magnetic field B(i) = 0.2 T
• Final magnetic field B(f) = 0.5 T
• Time Δt = 0.4 s
2. Calculate the change in magnetic flux:
Magnetic flux is Φ = B .A cos(θ). (Assume θ = 0°, so cos(0°) = 1)
Initial flux Φ(initial) = 0.2 * 0.03 = 0.006 Wb
Final flux Φ(final) = 0.5 * 0.03 = 0.015 Wb
Change in flux ΔΦ = 0.015 - 0.006 = 0.009 Wb
3. Calculate the rate of change of magnetic flux:
The rate of change of magnetic flux is dΦ/dt = ΔΦ / Δt = 0.009 / 0.4 = 0.0225 Wb/s
4. Apply Faraday’s Law:
Apply Faraday’s Law: EMF = -N * (dΦ/dt) = -150 * 0.0225 = -3.375 V
5. Final Answer:
The induced EMF is 3.375 V (the negative sign indicates the direction of the induced
current).