6) Electrodynamics: Electromagnetic induction and A.C

generator, alternator, or dynamo.

A machine that converts mechanical energy into electrical energy

According to Faraday's Law of Electromagnetic Induction

(Fara- day's Law: The induced electromotive force or EMF in any closed circuit is directly proportional to the rate of change of the magnetic flux (flux linkage) through the circuit.) an emf will be induced in a conductor if it is moved across the field lines of a magnetic field. The magnitude of the emf is proportional to the rate at which the field lines are cut. --> we produce emf most effectively when we have the greatest rate of cutting magnetic field lines.

Another way of stating Lenz's law

- Coils and loops like to maintain the status quo (i.e., they don't like change). - If a coil has zero magnetic flux, when a magnet is brought close then, while the flux is changing, the coil will set up its own magnetic field that points opposite to the field from the magnet.

Induction in a coil If you connect a coil of wire to a galvanometer (a sensitive device we can use to measure current in the coil). There is no battery or power supply, so no current should flow. Now bring a magnet close to the coil. You should notice:

- If the magnet is held stationary near/inside, the coil, no current will flow through the coil. If the magnet is MOVED, the galvanometer needle will deflect, showing that current is flowing through the coil.

Right hand rule:

- Point the thumb on your right hand in the direction of the required field, into the page in this case. If you curl your fingers, they curl in the direction the current flows around the loop - clockwise.

In the following example the permanent magnet moves to the left. What is the direction of the current through the resistor?

- The movement of the north end of the permanent magnet away from the solenoid induces electric potential in the solenoid. - To oppose the motion of the magnet, the left end of the solenoid becomes south, attracting the magnet. The attraction is not strong enough to prevent the movement; it just offers resistance to the movement.

A.C. generators In its simplest form an alternator or AC generator consists of...

- a coil that can be rotated in a magnetic field - two slip rings that are connected to the two ends of the coil. - The slip rings are connected to the external circuit (or to whatever machine or appliance operates off the alternator) through carbon brushes.

If the coil keeps on turning clockwise we will find it in the following position after a while:

- ab is moving into the page - cd moves out of the page. This means that current now flows from a to b and from c to d. current has reversed direction in each of the wires and therefore also in the coil. This reversal of current is what is meant by an alternating current.

Then how can emf be increased?

- turning then coil faster - and by using a stronger magnet.

B is measured in Tesla. 1 Tesla is equal to?

1 Tesla is equal to 1 N force on 1 m wire carrying a current of 1 A

WHY A.C? In S.A. Eskom supplies electricity at around _____. This is stepped down to _____ in intermediate transmission lines and is stepped down further to ____ for home use.

132000 V 6000 V 220 - 240 V

Explain by referring to the cutting of field lines why the graph for emf shows its maximum magnitude and minimum magnitude at the angles where you have drawn them.

A current will only be induced if there is a changing magnetic field When the angle is at 0: - the normal to the coil and the magnetic field are parallel to each other. There is a maximum magnetic flux, but no change in magnetic flux hence the emf is zero. When the coil is at the position of 90: the movement of the coil and the magnetic field are perpendicular to each other. The coil is therefore cutting the maximum number of magnetic field lines and there is the greatest change in magnetic flux linkage.

D.C. generator

A generator that produces a D.C. (Direct emf or Current) output

A.C. generator or alternator.

A generator that produces an A.C. (Alternating emf or Current) output

While the magnetic field is changing, the emf induced in the coil causes a current to flow. Does the current flow clockwise or counter-clockwise around the coil?

Apply Lenz's law AND right-hand rule. While the magnetic field is being changed, the magnetic flux is being increased out of the page. - According to Lenz's law, the emf induced in the loop by this changing flux produces a current that sets up a field opposing the change. - The field set up by the current in the coil, points INTO the page, opposite to the direction of the increase in flux. - To produce a field into the page, the current must flow clockwise around the loop. (right hand rule.)

The Generator and Faraday's Law Φ= BA cosƟ

B is the strength of the field - made larger by using a stronger magnet (larger field means field lines closer to- gether) A = area of the coil θ = the angle between the perpendicular to the plane of the loop and field direction.

Using the right hand rule for solenoids, we point the thumb of the right hand along the direction of the field through the solenoid (ie. to the right). When we "grab" the solenoid with our right hand, the fingers curl upward behind the solenoid and come over top the solenoid and down in front of the solenoid. This is the ___. Conclusion?

Direction of conventional current flow through the solenoid. (For electron flow use the left hand.) Since the current flows downwards in front of the solenoid, it must travel to the right through the resistor.

** Why is voltage stepped up?

Done to reduce the current over long distances, as more energy is lost if the current is greater (more friction between moving charge in the wire). Because VpIp = VsIs for an ideal transformer, - the current will decrease - if the voltage increases. A.C. also provides the high frequency that many electrical machines utilise (e.g. electrical clocks).

Take note that in the electric motor: In the Generator:

EM: electrical energy is converted to mechanical (kinetic) energy. G: mechanical energy is converted to electrical energy.

Why is it important for Eskom to maintain this frequency?

Many appliances are made to operate at this frequency or even use it to synchronise rotations. (e.g. CD players, clocks, printers)

When the magnet is moved one way (say, into the coil), the needle deflects one way; when the magnet is moved the other way (say, out of the coil), the needle deflects the other way.

Not only can a moving magnet cause a current to flow in the coil, the direction of the current depends on how the magnet is moved.

Graphically this cyclic nature of A.C. can be represented as fol- lows:

The graph for current versus time would look the same, as the current goes through the same cycle as the emf.

Faraday's Law:

The induced electromotive force or EMF in any closed circuit is directly proportional to the rate of change of the magnetic flux (flux linkage) through the circuit.

Lenz's law:

The induced emf generates a current that flows in a direction so as to set up a magnetic field to oppose the change in magnetic flux.

Explain how the shape of the graph for ф vs θ relates to the shape of the graph for ε vs θ.

The negative gradient of the ɸ vs θ graph is the induced emf.

Applying Lenz's Law When do we use Lenz's Law?

To determine the direction of the current produced when electric potential is induced,

Potential Difference is stepped UP over long distances: - to reduce the current - and therefore the loss of energy occurring in the wires due to friction that large currents cause. The energy lost in the conducting wires can be calculated by either:

V in this equation is not the input potential difference, but the drop in potential difference in the wire because of its resistance.

Assume that we now step the potential difference up to 100 000 V by using a transformer. Assuming an ideal transformer, there is no loss in power, which means Psupply at the start of the distribution line in the secondary coil of the transformer is still 20 000 W. We can now calculate the current. (**questions pg 96)

We therefore see much less loss in power and a smaller voltage drop across the distribution line.

If a wire loop is inserted in a magnetic field and the field is changed, what happens?

a current will be induced in the loop.

6.2 INDUCTION A changing magnetic field can induce (cause) _____. What does this mean, and what is it called?

an electric field This means that an emf can be created in a wire that experiences a changing magnetic field. This process is called electromagnetic induction.

A changing magnetic field can induce (cause) ____. ---> so an emf can be created in a wire that experiences a changing magnetic field.

an electric field This process is called electromagnetic induction.

Consider a coil rotating anti-clockwise in a magnetic field (B) The perpendicular to the area of the coil (the normal) is indicated when the coil is in different positions. The first three positions = X, Y and Z. In position X: the angle between the normal and the field (Ɵ) is 0, in position Y: it is 90 and in position Z: it is 180. Take note that the first position is arbitrarily chosen to be 0!. It could have been chosen to be 1800 in which case the graph would be the reflection around the horizontal axis of the one drawn be low.

arrow = direction of the magnetic field. X: the angle between the normal and the field (Ɵ) is 0 Y: 90 Z: 180.

As you may recall, transformers need a _____ for induction. This is made possible by the ___. This means that the A.C. cycle is completed every ___ or put another way, it means that the frequency of the cycle is ____

changing magnetic field alternating current (or emf) that changes direction every 0,01 s 0,02 s 50 Hz.

Electromagnetic induction requires a:

changing magnetic field;

This stepping down is done with transformers that operate on the principle of ____.

electromagnetic induction.

Faraday's law tells us that...

emf is proportional to the (negative) rate of change of flux, i.e. the negative of the gradient of the graph above.

Faraday's Law equation - increasing turns (N)... - decreasing Δt (turning faster) - Increasing ΔΦ by making the area of the coil bigger or the magnetic field stronger

explains the working of the generator. increasing turns (N)... will increase the emf. Making Δt smaller (turning faster) will increase the emf. Increasing ΔΦ by making the area of the coil bigger or the magnetic field stronger will also increase the emf.

See image Let's start by looking at the drawing alongside. The coil is being turned clockwise so that ab is moving out of the page and cd into the page. The magnetic field is (from.. to..) outside the magnet Apply Flemings right hand rule we see that the current flows from...

from N to S (top to bottom) - b to a - d to c.

Choose the picture that represents an A.C. generator.

left

NΦ is called the ____ and is the product of ____.

magnetic flux linkage the number of turns (N) on the coil and the flux (Φ) through the coil.

On the other hand, a coil with a particular flux from an external magnetic field will set up its own magnetic field in an attempt to...

maintain the flux at a constant level if the external field (and therefore flux) is changed.

So, if we draw tangents at each point,.. when the flux is at a maximum, the emf (gradient) is... and when the flux is at a minimum/zero, the emf is...

minimum/zero, maximum.

In both D.C. and A.C. generators, an emf is generated by...

rotating a coil in a magnetic field.

Len'z Law:

the induced current flows in a direction that opposes the change that induced the current.

Faraday's law of induction, states that...

the magnitude of the emf induced in a circuit is proportional to the rate of change of the magnetic flux that cuts across the circuit.

To explain the working of the alternator, we will look at the coil in different positions in the magnetic field. Fleming's left hand rule - determines the thrust that a current carrying conductor will experience in a magnetic field. but Fleming's RIGHT hand rule:

to determine the direction of induced conventional current when a conductor is moved in a magnetic field like the one above. - forefinger - magnetic field direction, - thumb = thrust - middle finger points in the direction of the induced current in the wire.

note cosθ is a maximum when

when θ = 0

cosθ= minimum (0)

when θ=90

Φ = BA cos θ

θ = angle between B and the normal of A. Φ = BA when the angle between the flux density (B) and the area (A) = 90 (when θ = 0).

If the flux (magnetic field strength) changes, an emf will be induced. 3 ways an emf can be induced in a loop:

• Change the magnetic field • Change the area of the loop • Change the angle between the field and the loop

Summarise scientific and economic reasons for A.C. in the national grid.

• Stepping up/down of potential difference requires transformers that operate on induction requiring a changing magnetic field. A.C. provides such a changing magnetic field. Many appliances make use of the frequency at which A.C. oscillates for their operation. Potential Difference is stepped UP over long distances: - to reduce the current - and therefore the loss of energy occurring in the wires due to friction that large currents cause.

According to Faraday's Law the emf can be increased by:

• increasing the rate at which the magnetic field changes • giving the coil more loops • increasing the area • using a stronger magnet