30.4: Motional Emf

Magnetic flux depends on three factors: the strength of the magnetic field, the area through which the field lines pass, and the field's orientation with respect to the surface area. If any of these quantities vary, a corresponding variation in magnetic flux occurs. If the area through which the magnetic field lines are passing changes, then the magnetic flux also changes. This change in the area can be of two types: the flux through the rectangular loop increases as it moves into the magnetic field, or the magnetic flux through the rotating coil changes.

If a conducting rod moves through a magnetic field perpendicular to the rod's motion, then an emf is induced in the rod. This induced emf produces an induced current when the conducting rod forms a closed conducting loop with a U-shaped conductor. The magnitude and the direction of the induced emf can be determined using Faraday's law and Lenz's law. In such systems, the conservation of energy demands that the power delivered because of the motion of the rod and the power dissipated because of the induced current are equal.

This principle can be seen in the operation of a rail gun. In a rail gun, the conducting rod is replaced with a projectile or weapon to be fired. In this type of gun, the optimal shutting off/ramping down of the magnetic field decreases the flux between the rails, causing a current to flow in the rod that holds the projectile. This current through the armature experiences a magnetic force and is propelled forward. Rail guns, however, are not used widely in the military due to the high cost of production and high currents.

Consider a conducting rod of length L moving with a constant velocity v in the magnetic field B that is pointing in the plane of the screen.

The magnetic force acting on a positive charge within a conducting rod is upward, resulting in opposite charges accumulating on either ends of the rod. This creates an electric field, in the downward direction.

The charges keep accumulating until the electric force is large enough to balance the magnetic force. The potential difference across the rod is present as long as it moves.

If this rod forms a closed conducting loop with a stationary U-shaped conductor, the free charges from the rod redistribute along the loop. This generates a current in the closed loop, and the moving rod generates a motional electromotive force known as a motional emf.

Here, the magnetic flux passing through the closed loop is equal to the magnetic field times the area of the loop. According to Faraday's law, the rate of change of magnetic flux is equal to the magnitude of motional emf.