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Electromagnetism Formula

What is Faraday's Law of Induction?

A changing magnetic flux induces an EMF — the foundation of generators, motors, and transformers.

Formula: \mathcal{E} = -\frac{d\Phi_B}{dt}

Plain-English Meaning

Move a magnet near a coil and a current flows — this is electromagnetic induction. The faster you wave the magnet (faster change in flux), the bigger the voltage induced. The minus sign (Lenz's law) means the induced current always opposes what's causing it — nature's way of resisting change.

Keep charge, field, potential, and current distinct. That single habit fixes a large fraction of electromagnetism errors.

Deeper Explanation

EMF ε = −dΦ/dt where Φ = ∫B·dA is the magnetic flux. For N turns: ε = −N dΦ/dt. Lenz's law is encoded in the minus sign. Generators convert mechanical rotation to EMF; transformers use mutual induction.

Worked Example

Problem: A coil of 200 turns sits in a field changing at 0.05 T/s through an area of 0.01 m². What EMF is induced?

  • Φ = BA = B × 0.01
  • dΦ/dt = (dB/dt) × A = 0.05 × 0.01 = 5×10⁻⁴ Wb/s
  • ε = −N dΦ/dt = −200 × 5×10⁻⁴ = −0.1 V

Result: EMF = 0.1 V (magnitude; minus sign indicates Lenz's opposition)

At A Glance

Category: Electromagnetism

Levels covered: High School, College, Masters, PhD

Best use: Start with the formula meaning, then move to the worked example and quiz so the equation turns into a tool instead of a memorised line.