UY1: Electromagnetic Induction Experiments

This page gives the UY1 working model/result for Electromagnetic Induction Experiments. You reuse it when you build fields/potentials by symmetry or superposition, and when you connect fields to forces, energy, and circuits.

Module path: Electromagnetism (UY1)
Practice: UY1 Electromagnetism Quiz
Full routing: UY1 Assessment Map
Math toolkit: Mathematics for Undergraduate Physics

1) At a glance

Main idea: induced current appears only when magnetic flux through a loop changes.
What changes flux: field strength B, loop area A, or orientation angle θ.
Core relation preview:

PhiB = int vecB · dvecA

Sign idea: the induced effect always opposes the change (formalized by Lenz’s law in the next lesson).
Modelling context: induction is a time-varying electromagnetic effect. A large steady B alone does not produce an induced current; you need dPhiB/dtne 0.

Prerequisites: Magnetic Field Lines & Magnetic Flux
Next uses: Faraday’s Law Of Induction & Lenz’s Law, Examples Involving Faraday’s Law

2) Setup

We compare three standard experiments with a coil connected to a galvanometer.

Move a bar magnet toward/away from a stationary coil.
Keep a current-carrying solenoid near the coil, then move one relative to the other.
Keep both stationary, but switch the solenoid current on/off.

Observation in all three cases: the meter deflects only while something is changing.

In most UY1 questions, the fastest decision is:

If flux through the circuit is not changing, the induced emf is zero.
If flux is changing, direction is decided by Lenz’s law after you choose a clear loop/area convention.

3) Core derivation/explanation

The unifying quantity is magnetic flux:

PhiB = BAcosθ

for a uniform field over a flat loop.

An induced e.m.f. appears when PhiB changes with time:

mathcalEᵢₙd ≠ 0 ⇌ dPhiB/dt ≠ 0.

So a current can be induced by:

changing B (move a magnet, change nearby current),
changing A (deform the loop),
changing θ (rotate the loop).

No change in flux means no induced current, even if B is large.

Units check:

Flux: PhiB in weber (Wb) where 1 Wb = 1 T m².
Rate of flux change: Wb/s, same as volts (V), which matches induced e.m.f. units.

Checks (what you should see in the experiments)

Move the magnet/coil faster Rightarrow larger |dPhiB/dt| Rightarrow larger meter deflection.
Reverse the motion (toward vs away) Rightarrow flip the deflection direction (the sign of dPhiB/dt changes).
Hold everything steady (even with a strong magnet nearby) Rightarrow no sustained deflection.

4) Worked example(s)

A 40-turn coil of area 3.0 × 10⁻³ m² is held fixed. A nearby field perpendicular to the coil rises from 0.10 T to 0.40 T in 0.050 s.

Magnitude of flux change per turn:

Δ PhiB = AΔ B = (3.0 × 10⁻³)(0.30) = 9.0 × 10⁻⁴ Wb.

Average induced e.m.f. magnitude:

|mathcalE| = NΔPhiB/Δ t = 40 · 9.0 × 10⁻⁴/0.050 = 0.72 V.

Interpretation: the galvanometer deflects only during the 0.050 s interval when B is changing.

5) Practice set (with hints + answers)

A loop stays fixed in a constant uniform magnetic field. Will there be induced current? Hint: check whether PhiB changes. Answer: No. dPhiB/dt = 0.
A loop area is doubled while B and θ stay constant. What happens to flux? Hint: PhiB = BAcosθ. Answer: Flux doubles.
A magnet moves faster toward a loop. Does induced e.m.f. magnitude increase, decrease, or stay the same? Hint: think about |dPhiB/dt|. Answer: It increases because flux changes more rapidly.

6) Summary + next steps

All induction experiments point to one rule: changing magnetic flux causes induced e.m.f.
Flux can change through field strength, area, or orientation.
The sign and direction are handled by Faraday’s law and Lenz’s law next.

Next: Faraday’s Law Of Induction & Lenz’s Law Previous: Applications Of Ampere’s Law Back To Electromagnetism (UY1)