## 34.1 Induced Currents

See Diagram on bottom of page 1042.

Faraday discovered that there is a current in coil of wire if and only if the magnetic field passing through the coil is Changing.

## 34.2 Motional Emf

EMF actually stands for "Electromotive Force".

"force" is not a force in the classical physics sense—as can be seen in the fact that it is measured in volts and not newtons.(Wikipedia)

"The magnetic force exerted on the charges in a moving conductor will generate a voltage (a motional emf). The generated voltage can be seen to be the work done per unit charge. This motional emf is one of many settings in which the generated emf is described by Faraday's Law. (from Hyperphysics - really good website - http://hyperphysics.phy-astr.gsu.edu/hbase/electric/elevol.html#c2)

The motion of the wire through a magnetic field induces a potential difference vlB between the ends of the conductor.

Motional emf versus chemical emf (Figure 34.3)

magnetic forces separate the charges and cause a potential difference between the ends. This is a motional emf

Chemical reactions separate charges and cause a potential difference between the ends. This is chemical emf.

The emf of a conductor is due to its motion, rather than to chemical reactions inside, so we can define the motional emf of a conductor moving with velocity v perpendicular to a magnetic field B ( a vector) to be: ε = vlB

#### Induced Current in a Circuit

two ways to create induced current:

(1) A motional e,f due to magnetic forces on moving charge carriers

(2) An induced electric field due to a changing magnetic field

#### Energy Considerations

Equations 34.6 and 34.7 give us an important information that: The rate at which work is done on the circuit exactly balances the rate at which energy is dissipated. Thus energy is conserved.

Three important points to consider:

(1) pulling or pushing the wire through the magnetic field at speed v creates a motional emf ε in the wire and induces a current I = ε/R in the circuit.

(2) to keep the wire moving at constant speed, a pulling or pushing force must balance the magnetic force on the wire. This force does work on the circuit.

(3) The work done by pulling or pushing force exactly balances the energy dissipated by the current as it passes through the resistance of the circuit.

#### Eddy Currents

a pulling force must be exerted to pull the loop out of the magnetic field.

See Figure 34.9

(a) no force is needed to pull the loop when the wires are outside the magnetic field.

(b) a pulling force is needed to balance the magnetic force on the induced current.

Eddy currents are electric currents induced in conductors when a conductor is exposed to a changing magnetic field; due to relative motion of the field source and conductor or due to variations of the field with time. This can cause a circulating flow of electrons, or current, within the body of the conductor (wikipedia's definition for Eddy Currents).

See Figure 34.10

(a) Eddy current are induced when a metal sheet is pulled through a magnetic field.

(b) magnetic force in the eddy currents is opposite in direction to v (a vector).

## 34.3 Magnetic Flux

Magnetic flux measures the amount of magnetic field passing through a surface.

$\Phi_m = \mathbf{A} \cdot \mathbf{B} = AB \cos \theta,$

Three ways to change the flux:

(1) A loop moves into or out of a magnetic field

(2) The loop changes area or rotates (the angle changes)

(3) The magnetic field through the loop increases or decreases

## 34.4 Lenz's Law

Lenz's Law

There is an induced current in a closed conducting loop if and only if the magnetic flux through the loop is changing. The direction of the induced current is such that the induced magnetic field opposes the change in the flux. (A magnetic flux can change in three ways as explained in previous section).

Figure 34.22 is AMAZING: It shows the induced current for sic different situations. It is very helpful when trying to determine what opposes what. You need to be able to apply those when doing questions involving Lenz's Law.

TACTIC BOX 34.1 using Lenz's Law(page 1053)

(1) Determine direction of magnetic field. The field must pass through the loop.

(2) Determine how flux is changing is it increasing, decreasing or staying the same?

(3) Determine the direction of an induced magnetic field that will oppose the change in the flux.

- Increasing Flux: induced magnetic field points opposite the applied magnetic field

- Decreasing Flux: induced magnetic field points in the same direction as the applied magnetic field

- Steady Flux: there is NO induced magnetic field

(4) Determine the direction of the induced current. use RHR (right hand rule) to determine the current direction in the loop that generates the induced magnetic field you found in step 3.

here comes the formal statement of Faraday's Law

An emf ε is induced around a closed loop if the magnetic flux through the loop changes. The magnitude of the emf is:

$\mathcal{E} = \left|{{d\Phi_B} \over dt} \right| \ ,$

Following is Print Screen from a very useful page on Hyperphysics: http://hyperphysics.phy-astr.gsu.edu/hbase/electric/elevol.html

FROM THIS POINT FORWARD, just attempt the Examples and the rest of Stop To Think questions 34.5 - 34.7 Read the answers and explanations in the back of textbook, For more clarification look up appropriate equations in that section. =D