What Is Electromagnetic Induction?
When a metal wire is connected to a battery, a current flows — electrons move along the wire. Place this wire in a magnetic field and an additional electric force is induced by the motion of electrons. This effect also works in reverse: stationary electrons placed in a changing magnetic field experience an induced electromotive force (EMF), and a current begins to flow. This phenomenon is called electromagnetic induction, and it is the foundation of generators, transformers, and electric motors.
Magnetic Field and Magnetic Flux
The magnetic field has two key characteristics:
- Magnetic flux density B — the strength of the field, measured in teslas (T) in the SI system, or gauss (G) in the CGS/American system (1 T = 10 000 G).
- Magnetic flux Φ — the total magnetic field passing through a surface, measured in webers (Wb) in SI, or maxwells (Mx) in CGS (1 Wb = 108 Mx).
Magnetic flux and flux density are related by the formula:
Φ = B × A × cos(θ)
where A is the cross-sectional area of the coil and θ is the angle between the magnetic field vector and the normal to the coil surface. When the field is perpendicular to the coil (θ = 0°), the flux is maximum: Φ = B × A.
The unit relationship: 1 Wb = 1 T × 1 m², or equivalently 1 T = 1 Wb/m².
Faraday's Law Formula
Faraday's law states that the EMF induced in a circuit equals the negative rate of change of the magnetic flux through the loop:
ε = −N × ΔΦ / Δt
where:
- ε — induced electromotive force (EMF) in volts (V)
- N — number of turns (loops) in the coil
- ΔΦ = Φ2 − Φ1 — change in magnetic flux in webers (Wb)
- Δt — time interval in seconds (s) over which the flux changes
The magnitude of the induced EMF is:
|ε| = N × |ΔΦ| / Δt
Lenz's Law
Lenz's law defines the direction of the induced current: the induced current always flows in a direction that opposes the change in magnetic flux that caused it. This is expressed by the minus sign in Faraday's formula. In practice, Lenz's law explains why generators resist rotation and why braking systems in electric vehicles work.
Unit Systems
| Quantity | SI (Metric) | CGS / American | Conversion |
|---|---|---|---|
| Magnetic flux density B | Tesla (T) | Gauss (G) | 1 T = 10 000 G |
| Magnetic flux Φ | Weber (Wb) | Maxwell (Mx) | 1 Wb = 108 Mx |
| Area A | m², cm², mm² | ft², in² | 1 ft² ≈ 0.0929 m² |
| EMF ε | Volt (V) | Volt (V) | — |
How to Use This Calculator
Choose one of two input modes:
- Enter flux change directly — provide the initial flux Φ1, final flux Φ2, and the time interval Δt. The calculator computes ΔΦ = Φ2 − Φ1 and then the induced EMF.
- Calculate from magnetic field — provide the initial field B1, final field B2, coil area A, and angle θ. The calculator first computes Φ1 = B1×A×cos(θ) and Φ2 = B2×A×cos(θ), then finds the induced EMF.
Results are shown in volts (V), millivolts (mV), and microvolts (μV) alongside the applied formula.