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medium difficulty10 min

Motional EMF in a Moving Conductor

Motional emf is the emf induced across a conductor moving through a magnetic field because charges in the conductor experience magnetic force. For a rod of length l moving with speed v perpendicular to a uniform magnetic field B, epsilon = Bvl.

In one line: Moving rod cuts flux; longer, faster, stronger field means larger emf.

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Understand it

When a conducting rod moves in a magnetic field, free charges experience force q v × B and separate at the ends of the rod. This charge separation creates a potential difference. If the rod is part of a closed circuit, induced current flows, and a magnetic force opposes the motion.

Example

A metal rod sliding on conducting rails in a magnetic field perpendicular to the rail plane develops emf across its ends. If the circuit is complete, current flows through the rod and rails.

Formula and rule

Formula: epsilon = Bvl for a straight conductor of length l moving with speed v perpendicular to uniform magnetic field B.

Here epsilon is motional emf in volt (V), B is magnetic field in tesla (T), v is speed of the conductor in metre per second (m s−1), and l is the effective length of the conductor in metre (m) that cuts the field lines.

Magnetic force on a current-carrying rod is F = BIl, where F is in newton, I is current in ampere, and l is the rod length in the field.

These simple forms assume mutually perpendicular B, v, and l.

See it worked out

Follow the example line by line, then use the same method on new questions.

Worked example

A rod of length 0.40 m moves at 5.0 m s−1 on rails in a uniform magnetic field of 0.25 T perpendicular to the plane. epsilon = Bvl = 0.25 × 5.0 × 0.40 = 0.50 V.

  1. 1If circuit resistance is 2.0 ohm, current I = epsilon/R = 0.50/2.0 = 0.25 A.
  2. 2The induced current appears because the moving rod changes the area and hence flux.

Method you can reuse

  1. 1Check perpendicular geometry.
  2. 2Write epsilon = Bvl.
  3. 3If resistance is given, find I = epsilon/R.
  4. 4For force, use F = BIl.
  5. 5Use Lenz's law to decide direction of current and opposing force.

Sketch it in your answer

Use a rectangular rail setup with a sliding rod, uniform magnetic field shown by crosses or dots, rod velocity v, induced current direction, length l, and magnetic force opposing motion.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

What happens to motional emf if the speed of the rod is doubled while B and l remain constant?

Think first, then show answer
The motional emf doubles because epsilon = Bvl. With B and l constant, emf is directly proportional to speed v.

Common wrong answer

Taking l as rail length instead of rod length, or forgetting that the magnetic force opposes the rod's motion when current flows.

Don't mix this up

Students often use epsilon = Bvl even when velocity, length, and magnetic field are not mutually perpendicular. The simple form applies directly only for the perpendicular arrangement.

Exam tip

Before substituting, check the geometry: B perpendicular to the plane of rails, rod length perpendicular to velocity, and rod moving steadily.

Write it in the exam

Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.

How CBSE asks it

It is asked as derivation of epsilon = Bvl, numerical calculation of emf or current, direction by Lenz's law, and force needed to keep the rod moving uniformly.
  1. 1

    Enough for 1 mark

    Motional emf is the emf induced across a conductor moving through a magnetic field because charges in the conductor experience magnetic force. For a rod of length l moving with speed v perpendicular to a uniform magnetic field B, epsilon = Bvl.

  2. 2

    Add for 2 marks

    Example: A metal rod sliding on conducting rails in a magnetic field perpendicular to the rail plane develops emf across its ends. If the circuit is complete, current flows through the rod and rails.

  3. 3

    Add for 3 marks

    When a conducting rod moves in a magnetic field, free charges experience force q v × B and separate at the ends of the rod.

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