Induced voltage in a moving conductor

Key ideas

Move a conductor through a magnetic field and a voltage appears across its ends — electromagnetic induction. The moving wire pushes the free charges inside it sideways, building up a potential difference. This is how a generator works.

The induced-voltage relationship

For a straight conductor of length $L$ moving at speed $v$ at right angles to a uniform field $B$:

$V = BvL$

• $V$ — induced voltage (V)
• $B$ — magnetic field strength (T)
• $v$ — speed of the conductor (m s⁻¹)
• $L$ — length of conductor in the field (m)

What increases the voltage

The induced voltage is bigger if:

• the field $B$ is stronger,
• the conductor moves faster ($v$),
• the conductor is longer ($L$), or
• the conductor cuts the field lines at right angles (maximum) rather than sliding along them (zero).

:::tip No movement across field lines means no induced voltage. A conductor held still in a field, or sliding along the field lines rather than across them, induces zero voltage — only the motion that cuts field lines counts. If $v = 0$, then $V = 0$. :::

Practice question

A $0.40$ m rod moves at $5.0$ m s⁻¹ across a $0.20$ T field. Find the induced voltage.

Worked solution: $V = BvL = 0.20 \times 5.0 \times 0.40 = 0.40$ V.