Ch 20Inductance and Faraday’s Law

1, 3, 4, 5, 7, 9, 10, 11, 17, 21, 25, 30, 31, 39, 41, 49

• The coil with the switch is connected to a battery. (Primary coil)

•When current goes through a coil, it produces a magnetic field.

•The coils are wrapped around an iron ring to intensify the magnetic field.

•The secondary coil is hooked up to an ammeter. This coil is not hooked up to a battery.

• When the switch in the primary coil is closed, the ammeter reads a current in the secondary coil for a short moment, then returns to zero.

• When the switch is opened, the ammeter momentarily measures a current in the opposite direction before returning to zero.

• When there is a steady current in the primary coil, there is no current read by the ammeter.

• emf–electric motive force, not really a force.

• This is a source of electrical work/energy per unit charge. Energy per charge = electric potentialwork/charge = volt

• Devices that increase the potential energy of circulating charges (batteries, generators) are sources of emf.

• Think of emf as a voltage increase.

The changing magnetic field induced an electric field in the secondary wire that caused the current to flow.

While the magnetic field inside the secondary coil was changing, the secondary coil acted as is it was connected to a battery.

Magnetic FluxThe value of the magnetic flux is proportional to the number of B-field lines passing through the loop.

B= B A cos θ is maximized when θ = 0. This is when the B-field is perpendicular to the loop.

see fig. 20.2, 20.3 for maximizing/minimizing the fluxwork example 20.1

Faraday’s Law of InductionConsider a wire loop connected to an ammeter.

Moving a magnet towards the loop will induce a current in one direction.

When the magnet is stationary, there is no induced current.

Moving the magnet away from the loop induces a current in the opposite direction.

This is similar to the Faraday experiment shown earlier.

Lenz’s Law: The induced current travels in the direction that creates a magnetic field with flux opposing the change in the original flux through the circuit.

If the flux is increasing in one direction, the induced current will be in the direction so that its own magnetic flux will be in the direction opposite of the original flux.

Nature wants to keep the flux constant.

Lenz’s Law has to do with the minus sign in Faraday’s Law.

See examples on pages 705 and 706 for different situations where we use Lenz’s Law.

Work out example 20.2 for quantitative example.

The induced magnetic flux does not have to be in the opposite direction of the original flux.

Fig. 20.5. The original flux is upwards. As the B-field is reduced in strength, the flux is reduced. Lenz’s law will show that the induced current will be in the direction so that the induced B-field is in the upward direction.

Applications of Faraday’s Law

• Ground fault interrupter – used to protect against short circuits

• Pickup on an electric guitar – converts the vibrations of a string to an electrical signal

• Electrical generator – uses changes in flux from a rotating object to produce electricity

Pictures on page 707

Figure 20.15

Now the conductor is part of a closed loop.

See pictures on page 709.

Conducting bar of length L slides along two fixed parallel conducting rails. Let the stationary part of the loop have a resistance R. A uniform and constant B-field is perpendicular to the plane of the loop.

As the bar is pulled to the right, a magnetic force acts on the free charges in the bar. Since the bar is part of a closed loop, an induced current circulates.

Lenz’s Law reviewed

Look at the situation to see how the magnetic flux is changing.

Determine the direction of the change of the flux.

The induced current will produce flux in the opposite direction of the change in flux.

Generators

Generators and motors operate on the principle of electromagnetic induction.

Generators converts mechanical energy to electrical energy.

Motors convert electrical energy to mechanical energy.

The net voltage across the resistor is the emf from the battery minus the induced emf. fig 20.23

The opposing emf results in a gradual increase in current.

When the switch is closed, the current does not immediately drop to zero either.

This effect is called “self-inductance”.

Inductance (L) proportionality constant between the induced emf and the rate that the current changes.

Depends on the geometric factors of the circuit involved.

Look at the example of a solenoid.Solenoid = described with the area, number of turns per length

Problem 49

Inductor carries 1.7 A of current, stores 0.3 mJ of energy.

Find the inductance.

Using the inductance, find how much energy is stored if the current is 3 A.