Motional EMF in a Moving Conductor

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

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.

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

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.

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. 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. 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.

When a conducting rod moves in a magnetic field, free charges experience force q v x 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. 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. 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 x 5.0 x 0.40 = 0.50 V. If circuit resistance is 2.0 ohm, current I = epsilon/R = 0.50/2.0 = 0.25 A. The induced current appears because the moving rod changes the area and hence flux. 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. Taking l as rail length instead of rod length, or forgetting that the magnetic force opposes the rod's motion when current flows.