Velocity selector

A charged particle with velocity v, moving through a region with both magnetic and electric fields at right angles.

Mass spectrometer

Magnetic fields due to a coil and solenoid

Induced e.M.F as a result of changing magnetic flux ф

Faraday’s Law of Induction

1. An e.m.f. is induced in a conductor when the magnetic field surrounding it changes;

2. The magnitude of the e.m.f. is proportional to the rate of change of the field;

3. The direction of the induced e.m.f. depends on the direction of the rate of change of the field.

N is the number of windings that make up the circuit

The minus sign comes from Lenz’s Law

Lenz’s Law of Induction

Lenz’s Law states that:

“the induced emf ε has such a direction as to oppose the change that has caused it”

OR

“the induced current will create a magnetic field in a direction that will oppose the change in the magnetic flux through the area A”

Lenz’s Law is a consequence of the conservation of energy

General Faraday’s Law

Let us recall that emf , is a voltage that is set up between two points in space by a changing magnetic flux . Therefore Faraday’s law can be written as:

Self-Induction

• Self-induction occurs when the changing magnetic field produced by the coil induces an e.m.f. in the same coil. An induced e.m.f. is proportional to the rate of change of the current:

• The constant of proportionality L is called self-inductance of the coil. Self-inductance depends only on the geometry of the coil and the number of turns.

Inductance of a solenoid (Derivation)

Unit of L: 1 H (Henry) = 1 V s /A

• For a Solenoid:

Lenz’s law illustration

• The magnetic flux due to the external magnetic field through the enclosed area increases with time.

• The induced current must produce a magnetic field out of the page.

• If the bar moves in the opposite direction, the direction of the induced current will also be reversed.

Motional Electromotive Force

• A motional emf is induced in a conductor that moves inside a constant magnetic field

• The electrons in the conductor experience a force that is directed along ℓ according to:

Motional Electromotive Force

Mechanical Power

• Consider the situation of the previous slide:

• Therefore the power of the mechanical force is equivalent to the power lost as heat in the circuit (assuming frictional effects to be negligible).

The Alternating Current (AC) generator

• The AC generator consists of a loop of wire rotated by an external force inside a magnetic field.

• It takes in energy by work and transfers it out by electrical transmission.

The AC generator

• The induced emf in the loop is:

• e_max occurs when wt = 90^o or 270^o

• This occurs when the magnetic field is in the plane of the coil and the time rate of change of flux is a maximum.

• e = 0 when wt = 0^o or 180^o

• This occurs when the magnetic field is perpendicular to the plane of the coil and the time rate of change of flux is zero.

The Direct Current (DC) generator

• It has essentially the same components as the AC generator

• The main difference is that the contacts to the rotating loop are made by a split ring called a commutator.

• The output voltage always has the same polarity.

• The current is a pulsing current.

• To produce a steady current, many loops and commutators around the axis of rotation are used.

• The multiple outputs are superimposed and the output is almost free of fluctuations.