Electromagnetic Induction
Understanding every component of the induced EMF equation through visual demonstrations.
Angular velocity
1. B = Magnetic Flux Density
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Full form: Magnetic Flux Density.
Magnetic flux density tells us how strong a magnetic field is at a particular location.
See a magnetic field
The blue lines represent magnetic field lines.
What happens when B increases?
Fewer field lines
Lower B
More field lines
Higher B
SI unit: Tesla (T)
Remember: More magnetic field strength means greater maximum EMF, if all other quantities remain constant.
2. A = Area of the Coil
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Full form: Surface Area Enclosed by the Coil.
Area tells us how much surface is enclosed by the conducting loop.
Visualise the area of a coil
A larger loop encloses a larger surface area.
Imagine both coils inside the same magnetic field
The same magnetic field passes through both coils. The larger coil encloses more magnetic flux.
Φ (Phi) is the Greek letter used to represent Magnetic Flux in electromagnetism.
For a coil whose area is perpendicular to the magnetic field.
SI unit: Square metre (m²)
3. ω = Angular Velocity
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Full form: Angular Velocity.
It measures how quickly the coil changes its angular position.
See the coil rotating
One rotation takes more time.
One rotation takes less time.
Understanding angular displacement
Angular velocity = Change in angle ÷ Time taken
Suppose a coil rotates through 90° in one second.
SI unit: Radian per second (rad/s)
4. sin(ωt) = Sine Function and Time
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This is the part that explains why EMF continuously changes its value and direction.
Understand a rotating coil through four positions
Imagine that one point on the coil is moving around a circular path. Its angular position determines the instantaneous EMF.
EMF = 0
EMF = +E₀
EMF = 0
EMF = −E₀
Watch the relationship between rotation and EMF
The orange point moves across the graph to represent the changing EMF. The wave shows one complete cycle.
Instantaneous EMF = Maximum EMF × Sine of angular position
5. f = Frequency
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Full form: Frequency.
Frequency tells us how many complete rotations occur in one second.
One rotation versus multiple rotations
Illustrative single-cycle pattern
Twice as many cycles in the same time
Frequency = 1 ÷ Time period
Here, T is the time required to complete one rotation.
If a coil completes 50 rotations in one second:
It produces 50 complete electrical cycles per second.
6. π = Pi and Complete Rotation
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Pi is a mathematical constant. It connects the circumference of a circle with its diameter.
Understand a complete circular rotation
One complete rotation is 2π radians. Therefore, if a coil completes f rotations every second, its angular velocity is:
7. How All Components Work Together
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- B determines the magnetic field strength.
- A determines the surface area enclosed by the coil.
- ω determines how quickly the coil rotates.
- f determines the number of rotations per second.
- π converts complete rotations into radians.
- sin(ωt) determines the instantaneous EMF.
Electromagnetic Induction Lab
A coil spinning in a magnetic field generates voltage. Press play, or drag the coil sideways to spin it yourself.
e = NBAω sin(ωt)
Adjust The Parameters
Adjust the parameters
Mark the peak, change a slider, and see how many times bigger or smaller it becomes.
One full rotation
Tap or drag on the graph to jump to any point in the rotation.
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