Mobile Conductors Consider conductor moving in a uniform

Mobile Conductors • Consider conductor moving in a uniform magnetic field. • A charged particle in the rod experiences a magnetic force: • The magnetic force causes the free charges in the rod to move; • An excess of positive charge is created at one end, and the excess of negative charge is created at the other end.

Compensating Electric Field • Charges concentrating at the ends of the rod create a compensating electric field; • Charges stop to move, when the electric and magnetic forces compensate each other: • Motion of the conducting rod in a magnetic field creates the potential between the ends:

Circuit with Moving Conductor • Consider the moving rod which slides along a stationary Ushaped conductor; • Potential difference Vab causes a current to flow in a circuit; • Thus, the magnetic field acting on the moving charges creates emf:

Changing Magnetic Flux • Due to the motion of conductor, the area of the loop changes: • The magnetic flux through the loop changes: • Thus: Changing magnetic flux induces the emf and the current in the loop

Direction of current • The current in the loop also creates a magnetic field; • Direction of current in the loop is such, that the created magnetic field "opposes" to the change of the magnetic flux (c. f. Lenz's law); • Taking into account such direction of the current: • Negative sign reflects the fact, that induced emf always opposes to the change of magnetic flux.

Changing Magnetic Flux and emf • We got for the emf in a loop with changing area: • This relation remains valid if the magnitude of the field changes instead of the area of the loop; • In general, this result is valid for any loop with changing magnetic flux;