Electromagnetic Induction Electromagnetic Induction and Power Transmissionand Power Transmission

PhysicsMontwood High SchoolR. Casao

Electromagnetic induction is the process of generating an electric current by varying the magnetic field that passes through a circuit.Oersted’s discovery that an electric current creates a magnetic field resulted in experimentation that led to Faraday’s discovery of induced currents.

Faraday was experimenting with two coils of wire wrapped around an iron ring. He hoped that the magnetic field generated in the coil on

the left would induce a magnetic field in the

iron and that the magnetic field in the iron might create a current in the circuit on the right.

The technique failed to generate a current.Faraday noticed that the needle of the current meter jumped slightly at the instant when he closed the switch in the circuit on the left.After the switch was closed, the needle immediately returned to zero.The needle again jumped when he later opened the switch, but this time in the opposite direction.Faraday recognized that the motion of the needle indicated a very slight current in the circuit on the right.

The effect happened only during the brief interval when the current on the left was starting or stopping, not while the current was steady.

Faraday’s observation that the current meter needle jumped only when the switch was opened and closed suggested that a current was generated only when the magnetic field was changing as it passed through the coil.Faraday’s law: there is a current in a coil of wire if and only if the magnetic field passing through the coil is changing.

The strength of the magnetic field can be changed.The area of the coil through which the magnetic field lines pass can be changed.

The EMF that accompanies the current induced in a coil of wire is given by:

N is the number of coilsThe negative sign appears because the EMF that is generated in the wire is in a direction that opposes the change in the number of magnetic field lines that pass through the area of the coil (this is called Lenz’s law). If the magnetic field strength changes over time:

If the area of the coil changes over time:

d B AEMF N

dt

fi

fi

B Bd BEMF N A N A

dt t t

fi

fi

A Ad AEMF N B N B

dt t t

Electromagnetic Induction (a) When there is no relative motion between the magnet and the wire loop, the number of field lines through the loop (in this case, 7) is constant, and the galvanometer shows no deflection.(b) Moving the magnet toward the loop increases the number of field lines passing through the loop (now 12), and an induced current is detected. (c) Moving the magnet away from the loop decreases the number of field lines passing through the loop (to 5). The induced current is now in the opposite direction. (Note the needle deflection.)

It makes no difference what causes the magnetic field to change:

current stopping or starting in a nearby circuit;moving a magnet through the coil; ormoving the coil in and out of a magnet.

In all cases the effect is the same; there is no current if the field through the coil is not changing.It is not the magnetic field itself that is responsible for the current, but the changing of the magnetic field.

Relative motion and no induction: when a loop is moved parallel to a uniform magnetic field, there is no change in the number of field lines passing through the loop, and there is no induced current

The current in a circuit due to a changing magnetic field is called an induced current.

Opening the switch or moving the magnet induces a current in a nearby circuit.An induced current is not caused by a battery.

Application: magnetic data storage encodes information in a pattern of alternating magnetic fields.

When the fields move past a small pick-up coil, the changing magnetic field creates an induced

current in the coil.The current is amplified into a

sequence of voltage pulses that represent the 0’s and 1’s of digital data.

Motional EMFAn induced current is created in two different ways:1. By changing the size or orientation of a circuit in a

stationary magnetic field.2. By changing the magnetic field through a stationary circuit.Consider a conductor of length l that moves with velocity v through a uniform

magnetic field B.The charge carriers inside the

wire also move with velocity v, so they experience a magnetic force FB = q·v·B.

This causes the charge carriers to move, separating the positive and negative charges.The separated charges then create an electric field inside the conductor.

The charge carriers continue to move until the electric force FE = q·E exactly balances the magnetic force FB.This happens when the electric field strength is E = v·B.

The magnetic force on the charge carriers in a moving conductor creates an electric field E = v·B inside the conductor.The electric field creates an electric potential difference between the two ends of the moving conductor.Equation: EMF = v·l·BThe motion of the wire through

a magnetic field induces a potential difference EMF = v·l·B between the ends of the conductor.

The potential difference depends on the strength of the magnetic field and on the speed of the wire through the field.

The EMF of a battery refers to the work done per charge to separate

the charges. A battery, where the charges are separated by chemical reactions is a source of chemical EMF.A moving conductor develops a potential difference because of the work done by magnetic forces to separate the charges.You can think of the moving

conductor as a battery that stays charged only as long as it keeps moving but runs down if it stops.

The EMF of the conductor is due to its motion and is called motional EMF.

The motional EMF of a conductor moving with velocity v perpendicular to a magnetic field B is: EMF = v·l·BThe moving conductor has an EMF, but it cannot sustain a current because the charges have nowhere to go.It’s like a battery that is

disconnected from a circuit.Consider a wire sliding with

speed v along a U-shaped conducting rail. The rail is fixed and cannot move.

The wire and the rail together form a closed conducting loop – a circuit.

Suppose a magnetic field B is perpendicular to the plane of the circuit.Charges in the moving wire will be pushed to the ends of the wire by the magnetic force, but now the charges can continue to flow around the circuit.The moving wire acts like a battery in a circuit.The current in the circuit is an induced current.The induced current is counterclockwise in the example.

If the resistance of the circuit is R, the induced current is given by Ohm’s law:

The induced current is due to magnetic forces on moving charges.

A continuous pulling force Fpull is required to keep the wire moving along the rail at constant speed.

The moving wire, which now carries induced current I is in a magnetic field and the magnetic field exerts a force F = I·l·B on the wire.

EMF v BI

R R

l

According to the right-hand rule, the magnetic force Fmag on the moving wire points to the left.This magnetic drag will cause the wire to slow down and stop unless we exert an equal and opposite pulling force Fpull to keep the wire

moving.The force required to pull the

wire with a constant speed v is:

2 2

pull mag

pull mag

pull mag

F F I B

EMF v BI

R Rv B

F F BR

v BF F

R

ll

l l

l

Energy ConsiderationsWork must be done on the wire to pull it.Power is the rate at which work is done on the wire.The power exerted by a force pushing or pulling an object with velocity v is P = F·vThe power provided to the circuit by pulling on the wire is:

The circuit also dissipates energy by transforming electric energy into the thermal energy of the wires and the components, heating them up.

2 2 2 2 2

input pullv B v B

P F v vR R

l l

The power dissipated by current I as it passes through resistance R is P = I2·RPower dissipated by the circuit is:

The rate at which work is done on the circuit exactly balances the rate at which energy is dissipated.Energy is conserved.

Summary1. Pulling or pushing the wire through the magnetic field at

speed v creates a motional EMF in the wire and induces a current in the circuit.

2 2 2 22

dissipatedv B v B

P I R RR R

l l

EMFI

R

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 the pulling or pushing force exactly balances the energy dissipated by the current as it passes through the resistance of the circuit.

There are two different ways to induce a current in a conducting loop:1. The loop can move or rotate or change size, creating

a motional EMF.2. The magnetic field strength B can be changed.

GeneratorsA slide wire pulled through a magnetic field on a U-shaped track is a simple generator because it transforms mechanical energy into electric energy.

In a more practical generator, a coil of wire is rotated in a magnetic field.

Both the magnetic field and the area of the loop are constant, but the number of magnetic field lines passing through the area of the loop changes continuously as the loop rotates.

Changing the number of magnetic field lines passing through the area of the loop changes the strength of the magnetic field through the loop.

The induced current is moved from the rotating loop by brushes that press up against slip rings.

The EMF generated by the change in the number of magnetic field lines that passes through the rotating loop is given by:

ω is the angular frequency (ω = 2·π·f) with which the coil rotatesA is the area of the coilB is the strength of the magnetic fieldN is the number of turns or windings in the coil

The sign of the EMF alternates between positive and negative as the angle = ω·t changes (remember that the sin is positive in quadrants I and II and negative in quadrants III and IV).Maximum EMF: EMF = ω ·N·A·B

sinEMF A B N t

Because the EMF alternates in sign, the current through the resistor R alternates back and forth in direction.The generator is an alternating-current generator producing an AC voltage.

AC OutletReceptacles have three holes eachLower (rounded) hole is the ground

connected to pipes, etc.green wire

Larger slot is “neutral”for current “return”never far from groundwhite wire

Smaller slot is “hot”swings to +170 V and 170 Vblack wiredangerous one

TransformersThe transformer has two

coils wrapped on an iron core.

The left coil is called the primary coil.

The primary coil has N1 turns and is driven by an oscillating voltage V1·cos (ω·t).

The magnetic field of the primary follows the iron core and passes through the right coil, which has N2 turns and is called the secondary coil.

The alternating current through the primary coil causes an oscillating magnetic flux through the secondary coil and an induced EMF.

The induced EMF of the secondary coil is delivered to the load as the oscillating voltage V2·cos (ω·t).

Faraday’s law tells us that the voltage V1 across the primary coil is equal to the number of turns N1 multiplied by the changing number of magnetic field lines passing through the area of the

primary coil:1 1

BdV N

dt

ΦB is the changing number of magnetic field lines passing through the area of the primary coil.The number of magnetic field lines that pass through the primary coil remain within the iron core and pass through the secondary coil.The voltage across the secondary is:

2 2Bd

V Ndt

1

1

2

2

21

1 2

B

B

d Vand

dt N

Vddt N

VVN N

If the secondary coil has more windings than the primary coil (that is Ns/Np > 1), the voltage is stepped up because Vs > Vp and this is called a step-up transformer.There is less current in the secondary than in the primary.If the secondary coil has fewer turns than the primary does (Ns/Np < 1), we have a step-down transformer.The voltage is stepped down and the current is increased (Is < Ip).

Transformers are used to transmitting power over long distances.The generator voltage is stepped up so the current in the transmission line is small, therefore, power losses to Joule heating (P = I2·R) are reduced.Voltages are stepped up to around 230000 V at the generating station, stepped down to about 20000 V at a distributing station, then down to 4000 V for delivery to residential areas, and finally to 120 V to 240 V at the customer’s site.

Power Consumption in WiresPower Consumption in WiresReminder:power consumption = current × voltage drop

voltage = resistance × current

power consumption = resistance × current2

So?Wires waste power as Joule heatDoubling current quadruples wasted powerBetter not transmit high current!

Power TransmissionPower TransmissionPower to primary coil = Power to secondary coilPin = Pout; Pprimary = Psecondary; Iin·Vin = Iout·Vout

Power delivered to a city is: power delivered = current × voltage drop

Power wasted in transmission wires is:power wasted = resistance × current2

For efficient power transmission:Use low-resistance wires (thick, short copper)Use low current and high voltage drop

This can be accomplish this with AC (alternating current) power transmission.