Electromagnetic Induction — Part 2: Motional emf and inductance: visual lesson, CBSE Class 12 Physics

Lesson

Motional emf and inductance

Part 2 — the emf in a moving conductor, and how coils induce emfs in themselves and in each other.

In this lesson you will

Derive the emf induced in a rod moving through a magnetic field
Define self-inductance and state the factors it depends on
Define mutual inductance and state the factors it depends on

Diagram

Motional emf in a sliding rod

Directions checked with q v × B and I l × B.

A rod of length $l$ slides with speed $v$ on rails, perpendicular to a uniform field $B$ . The area of the circuit grows at rate $lv$ , so $\varepsilon = \dfrac{d\Phi}{dt} = \dfrac{d(Blx)}{dt} = Blv$

Charge picture: each free charge in the rod feels $q\vec v \times \vec B$ along the rod, which drives the current.
With resistance $R$ : $I = Blv/R$ .

Worked example

Worked example 4: rod, current and force

A rod 0.50 m long slides at 4.0 m s $^{-1}$ on rails in a field of 0.30 T; the circuit resistance is 2.0 Ω. Find the emf, the current, the force needed to keep the rod moving steadily, and the power.

Step 1 — $\varepsilon = Blv = 0.30 \times 0.50 \times 4.0 = 0.60$ V; $I = \dfrac{0.60}{2.0} = 0.30$ A.
Step 2 — magnetic force on the rod $IlB = 0.30 \times 0.50 \times 0.30 = 0.045$ N, opposing the motion, so the same push is needed.
Step 3 — mechanical power $Fv = 0.045 \times 4.0 = 0.18$ W $= I^2R = 0.18$ W.

Directions checked with q v × B and I l × B.

Cookies