D.4.3 (HL)—Motional emf

Use the motional-emf model

A straight conductor of length $L$ moving at speed $v$ perpendicular to a uniform magnetic field $B$ sweeps out area and develops an emf. The stated equation is restricted to the perpendicular geometry.

\varepsilon=BvL

Worked example — moving conductor

For $B=120\,\mu\mathrm{T}=120\times10^{-6}\,\mathrm{T}$ , $v=98.0\,\mathrm{cm\,s^{-1}}=0.980\,\mathrm{m\,s^{-1}}$ and $L=23.0\,\mathrm{cm}=0.230\,\mathrm{m}$ , $\varepsilon=BvL=2.70\times10^{-5}\,\mathrm{V}$ . Reversing either motion or field reverses polarity.

Check the motion

The conductor must cut across field lines. Motion parallel to the field produces no motional emf; increasing B, v or the length in the field increases the emf. For a complete circuit, the emf can drive current.

Explain charge separation

Moving charge carriers in the conductor experience magnetic force and separate until an internal electric force balances it. The resulting potential difference across the ends is the motional emf.

Common trap

Do not use the wire’s total length if only part is inside the field, and do not expect emf when the motion is parallel to the field lines.

How it is assessed

Questions derive V=vBL or infer speed from voltage across a moving bar/rail system.

Command terms

Show / What is

What earns marks

Use ε=BvL for perpendicular motion, identify the active length in the field, and connect it to swept area or charge separation.

Watch for

Using a conductor length outside the field, or failing to recognize ΔA/Δt=Lv.

Representative question

[Maximum number: 3]

Show, using Faraday's law or otherwise, that the potential difference, V, established between the ends of the rod is V=v B L.

ALTERNATE 1

In time $\Delta t$ , rod moves a distance $v \Delta t$

Flux increases by $B(L v \Delta t)^{}$

«By Faraday» induced emf is the rate of change of flux: $\frac{B L v \Delta t}{\Delta t}$

«=BLv»

ALTERNATE 2

<<From $\varepsilon=-\frac{N \Delta \Phi}{\Delta t} \gg$

Recognition that $\Phi=B A$

Recognition that N = 1

Recognition that $\frac{\Delta A}{\Delta t}=L v \vee$

<<Leading to V=vBL OR $\varepsilon=\mathrm{BLv}>$

ALTERNATE 3

«In steady state» electrons stop drifting and so net force is zero q v B=q E

Substitution of $E=\frac{V}{L}$ to get result

ALT 1: Correct MP2 scores MP1

ALT2:

V and $\varepsilon$ are interchangeable. Ignore negative sign.

[3]

D.4 induction is secure when you connect geometry, rate of change and direction.

Magnetic flux: Φ=BA cosθ
Changing flux linkage induces emf by Faraday’s law
Motional emf: ε=BvL for a perpendicular moving conductor
Lenz’s law gives induced direction and reflects energy conservation
A rotating coil produces sinusoidal emf
Faster rotation shortens the period and increases peak emf when other variables are fixed

D.4.3 (HL)—Motional emf

Model Motional Emf

D.4.3 (HL) Exam Analysis

Assessment in practice

Retrieve the D.4 Induction Model

Question 1