Induced Voltage and Inductance When the switch is closed it causes a temporary current to flow in the secondary coil. Opening the switch again causes a current to flow. Ammeter Switch Iron Ring + Battery A - Primary Coil Secondary Coil

Induced emf When the current flows in the primary coil a magnetic field is produced. This in turn causes a temporary current to flow in the secondary coil. The ammeter reads only for a brief time and then returns to zero. When the switch is opened the ammeter reads a current in the opposite direction for a brief moment, indicating a magnetic field in the opposite direction. The magnetic field must keep changing to produce a current

Magnetic Flux An electric current can also be created if a loop conductor is rotated in the presents of a stationary magnetic field. ( a generator) Magnetic flux is a measure of how much magnetic field influences a surface. Magnetic Flux B = BA cos ( webers) where B = magnetic field A = area of loop  = the angle field makes to the normal of the area If B is perpendicular to A  = 0o

Faraday’s Law of Induction If a loop is moved toward or away from a stationary magnetic field, or a magnet is moved towards or away from a stationary loop an electric current will be produced. This relative motion produces an induced current. Faraday’s Law of magnetic induction states that the induced emf E =-N(B)/t where N is the number of turns in the loop.

Cont. Because B = BA cos any change in B A or  with time produces an emf. The minus sign indicates (polarity) the two different directions the current flows in the loop.

Motional emf Motional emf is the emf induced in a conductor as it moves through a magnetic field. Thus changing a loop’s area induces a current in a closed circuit. Current Sliding bar The sliding bar moves trough x increasing A of the loop B R l Magnet field into the page x l is the length of the moving bar

Cont. For the above diagram as the bar moves through x in time t, the increase in flux in that time is the amount of flux that passes through lx that is B = BA = Blx therefore E = B/t =Bl(x/t) = Blv As E = IR = (Blv)/R

Lenz’s Law Lenz’s law states that the direction of the induced emf is such that if an induced current were able to flow, it oppose the change that causes it. In the above diagram as the bar moves to the right the flux is increased into the page. To offset this the induced current must flow counterclockwise.If the bar is moved to the left current would flow clockwise. Induced current tends to maintain the original flux.

AC Generators An alternating current generator is a device that turns mechanical energy into electrical energy. It consists of a wire loop that is rotated in a magnetic field. Consider a loop of area A with N number of loops in a magnetic field of B moving at an angular speed of  then E=NBA sin t when t = 90o or 270o then E= Emax=NBA 

DC Generator DC generators are essentially the same as AC generators except that contact with the rotating loops are made with split rings so as to produce a changing magnetic field which allows for continual rotation.

Motors and back emf A motor is basically a generator in reverse. That is a current is supplied to a loop by an emf source and the magnetic torque on the loop causes it to rotate. As the loop rotates changing magnetic flux induces an emf which reduces the current in the loop, (lenz’s law). Back emf is this reduced current which reduces the overall emf.

Cont. When a loop starts to rotate there is no back emf. However after maximum rotation is achieved back emf is established Supplied emf is Esupplied = E- Eback When the motor starts initially with no back emf the current is large. As the loop rotates back emf opposes the applied voltage and the current is reduced.

Self Inductance Consider a circuit with a switch, a resistor and an emf source. When the switch is initially closed the current is not at maximum, it takes time to build, as does the magnetic flux in the loop. The increasing flux in the loop produces an induced emf that opposes the source emf, (Lenz’s Law). The net emf across the resistor is the emf of

Cont. The battery minus the induced emf. This opposing emf results in a gradual increases in current. As the magnitude of the current increases the opposing emf decreases. The same occurs when the switch is opened, the current does not immediately fall to zero. This effect is called self induction because the changing flux through the circuit is caused by the circuit.

Cont. The emf that is set up in a circuit by the circuit is called self-induced emf and is given by emf = Δv = -LΔI/Δt where L is a proportionality constant called inductance of the device. The negative sign indicates that the changing current induces an emf in opposition to the change.

Cont. The SI unit for inductance is a Henry (H) 1 H = 1 V.s/A As emf = -N(B)/t = -LΔI/Δt then L = (N B)/I For a solenoid of cross-sectional area A and length l L=( µoN2A)/l = µon2V Where n = number of turns per unit length V = volume of solenoid

RL Circuits Resistance is a measure of opposition to the current Inductance is a measure of the opposition to the rate of current change. The time constant of a circuit is the time required for the current in a circuit to reach 63.2% of its final value of I τ = L/R

Energy Stored in a Magnetic Field Inductor induced emf prevents a battery from establishing instantaneous current. The battery must do work to establish current as equating it to energy stored in the inductor PEL = ½ LI2