1: Review of essential concepts

motors and

generators

An electric current is defined as the rate of flow of net charge through

a region. In the wire in Figure 4.1.1, a number of electrons will flow through the

area A each second, and each electron carries a charge of –1.6 × 10–19 coulombs.

If the current is 1 ampere (or 1 amp), it carries 1 coulomb of charge per second

through area A, which is more than 6 billion billion electrons each second.

We now know that the nature of an electric current is actually a flow of electrons.

However, in electric circuits we often consider currents as if they were a flow of

positive particles. This type of current is called conventional current and it is in the

opposite direction to the flow of the negatively charged electrons. This confusing

situation has arisen because current was first thought to be a flow of positive particles.

Conventional methods for determining the direction of other physical quantities,

such as magnetic fields and forces, have been developed using the conventional

direction of current. So we will stick with these historical conventions.

It is important throughout this module to consider the direction of an

electric current as the direction in which a positive charge would flow through a

conductor. In Figure 4.1.1, conventional current flows from the positive terminal

towards the negative terminal, as indicated by the arrow along the wire.

An electrical current in which the charges only flow in one direction is

called direct current (DC). This current is commonly used in small portable

electronic devices and is supplied by a battery. One way of illustrating this type

of current graphically is shown in Figure 4.1.2.

The red line on the graph is a direct current measured by a digital ammeter.

The sign of the current (+ or –) represents the direction in which the current is

travelling. You can see that in this example the current has a constant value and

direction over time.

In contrast to direct current, an alternating current (AC) is continually

changing direction. The sign of the terminal at each end of an AC circuit

alternates between positive and negative over time. Each time this occurs, the

electric field within the wire changes direction. This reverses the direction of the

force on the charges within the wire and the current changes direction accordingly.

This type of current is good for transporting electrical energy over large distances

and is commonly used in larger appliances. In Figure 4.1.2, an AC current

measured by a digital ammeter is shown as a blue line. As the current changes

direction the blue line moves above or below the horizontal

axis. The corresponding change in sign of the current

indicates a change in the current’s direction.



Potential difference, emf and voltage

The work done by any electrical device can be traced back to

the creation of a difference in electrical potential energy. In

Figure 4.1.1, a chemical reaction separates the charges inside

the battery. This causes a difference in electrical potential

energy between the positive and negative terminals of the

The battery energy given to each coulomb

battery.

of charge within the battery is measured in volts and is

commonly called an emf (ε). In an ideal battery it is equal to

the voltage measured at the terminals when the battery is not

connected to a circuit. For this type of battery this is usually

about 1.5 V.



–



area

A



–



–



–



+



–

Figure 4.1.1 A battery creates an electric

field within the wire and

a current flows.



DC



+

AC

Current (A)



Direct current and alternating current



copper wire



0



10 20



30



40



50



Time

(ms)



–



Figure 4.1.2 A graph of AC and DC over time



Flick of a switch



T



he charges in a current-carrying wire travel along

the wire much more slowly than the speed at

which you normally walk. Why then does a light

come on instantly when you flick the switch? All the

free electrons in the wire start moving at the same

time under the influence of the electric field in the

wire. When you flick the switch, this field travels

along the wire at close to the speed of light. Almost

instantly all the free electrons are moving and losing

energy in the light bulb.

85



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Electrodynamics:

moving charges

and magnetic fields



Birds on a wire



H



ave you ever wondered why

birds can happily sit on

power lines and not get

electrocuted? No, those wires are

not insulated. For a current to

flow through a bird on a wire,

there would have to be a potential

difference between its feet. If the

bird could stand on the wire and

touch any other object such as

the ground or another wire then it

would get the shock of its life.



Figure 4.1.3 There is no potential

difference between

the bird’s feet.



When a wire is connected to the battery’s terminals (see Figure 4.1.1), an

electric field is set up within the wire. The electric field drives electrons from the

negative terminal, through the wire to the positive terminal. As the electrons

move through a circuit element, such as a light bulb, they collide with the ions in

the metal lattice. During these collisions they lose kinetic energy to the metal

lattice. The metal lattice then loses this energy as heat; in the light bulb it is also

lost as visible light.

The energy lost in the circuit element corresponds to a loss of electrical

The difference in potential

potential energy by the charges in the current.

energy per unit of charge between the two points either side of a circuit element

is known as the potential difference, potential drop or voltage (V). We can

measure this potential difference by connecting a voltmeter to the circuit in

parallel with the circuit element.



Resistance and Ohm’s law

Recall that the structure of a metallic conductor is essentially a lattice of metal

atoms (or ions) surrounded by a ‘sea’ of free electrons. If a potential difference V

is established within the metal, these free electrons will flow as a current I.

The amount of current that flows due to this potential difference is

V

determined by the electrical resistance of the material, which is defined by R =

I

and measured in ohms (Ω). A material that has a relatively high resistance

will only conduct a relatively small current for a given potential difference.

The resistance in a conductor is a result of the collisions of the moving

charges with the ions of the metal lattice. Basically, the more collisions the free

electrons have with the lattice the higher the resistance. Recall that the length,

cross-sectional area, temperature and type of material within the conductor

influence resistance.

In many circuit components, the ratio of voltage divided by current is a

This relationship is known as Ohm’s law and describes the

constant.

relationship in which V and I are proportional for a circuit, or circuit

component, with a fixed resistance R.



Resistance and power

The wire filament of the light bulb in Figure 4.1.1 has a very high resistance and,

therefore, a large amount of the available energy within the circuit is lost within

the bulb. This energy heats the filament in the blub to such a high temperature

that it emits visible light.

Whether energy in a circuit is lost as heat or in turning an electric motor, the

rate at which energy is converted into another form is called electric power P :

Power =



energy transferred

time taken for transfer



Recall that:

P = IV

V2

Substituting Ohm’s law V = IR: P = I 2R or P =

R

where P is power in watts (W).

Watts are equivalent to joules per second (J s–1), so we can determine the

energy lost:

Energy = Pt

where energy is in joules (J) and time is in seconds (s).

86



motors and

generators



Magnetic fields produced by electric currents

A magnetic field exists in a region of space if a magnet at some point in that

space would experience a magnetic force. From in2 Physics @ Preliminary

section 12.3, you know that a current-carrying conductor produces a magnetic

field. You can observe this circular magnetic field around a current-carrying wire

if you place a magnetic compass needle at various locations around the wire

(see Figure 4.1.4).

We represent magnetic fields by solid lines, called magnetic field lines, and

label these lines with the symbol B. These lines represent the places where the

magnetic field has the same strength. We also place arrow heads along these

By convention,

magnetic field lines to indicate the direction of the field.

the arrow heads indicate the direction in which the north pole of a magnet

would point within the magnetic field (see the compass needles in Figure 4.1.4).

You can work out the direction of the magnetic field in Figure 4.1.5

by using the right-hand grip rule. Grip the wire with your right hand and

point the thumb in the direction of the conventional current along the wire.

Remember, this is the direction in which positive particles would flow, from the

positive to the negative terminal. Your curled fingers will now point in the

direction of the magnetic field around the wire.

There are several conventions we need to recall when we draw twodimensional diagrams showing currents and magnetic fields. For example, when

we view the situation shown in Figure 4.1.5 from above, we represent this as

shown in Figure 4.1.6. The  symbol in the centre indicates that the current is

coming towards you (out of the page). When viewing the situation from below,

we represent this as shown in Figure 4.1.7. The  symbol in the centre indicates

the current is flowing away from you (into the page). Notice that the magnetic

field lines shown in Figures 4.1.6 and 4.1.7 are drawn more closely near the wire,

where the field becomes stronger.

The  and  symbols indicate that the current is flowing out of and

into the page respectively. You can remember this convention if you imagine that

 is the head of an archer’s arrow coming out of the page at you. The crossed

feathers in the back of the arrow are represented by , indicating that the arrow

is pointing away from you.

We also represent magnetic fields in two-dimensional diagrams as shown in

To show that the magnetic field points into or out of the

Figure 4.1.8.

page, we use  or  • respectively. Use the right-hand grip rule to determine the



B



Figure 4.1.6 Magnetic field lines around

a conventional current going

out of the page



I



B



Figure 4.1.4 A straight wire carrying a

current deflects the compasses

around it in a circular pattern.

electric current I



magnetic field B



Figure 4.1.5 The curled fingers point in the

direction of the magnetic field

when the thumb points in the

direction of the conventional

current along the wire.



B



Figure 4.1.7 Magnetic field lines around

a conventional current going

into the page

87



4



Electrodynamics:

moving charges

and magnetic fields

conventional current I



B



B



Figure 4.1.8 Magnetic field lines into ()

and out of (•) the page for a

wire carrying a conventional

current upwards in the plane

of the page



B

–



(a)



+



direction of the magnetic field around the wire in Figure 4.1.8. You should see

that the magnetic field lines would go into the page on the right-hand side of the

wire (represented by ) and come out of the page on the left (represented by •).

An extension of the situations you have reviewed above is the magnetic field

around a current-carrying wire loop. Again we use the right-hand grip rule to

determine the direction of the magnetic field around the current-carrying wire

(Figure 4.1.9). Notice that the magnetic field in the centre of the loop always

points in the same direction, no matter where your hand is around the loop.

In the following chapters there are many situations that involve loops of wire

carrying currents; therefore, it is important you are familiar with the magnetic

field that is produced around them.

Most applications of magnetic fields in current-carrying wire loops actually

involve more than one loop. Each loop is called a turn, and many turns together

are known as a solenoid (Figure 4.1.10). A solenoid is simply a long coil of wire,

and the magnetic field produced is similar to that of a bar magnet, with a north

The direction of the magnetic field through

and south pole at each end.

the centre of the solenoid is determined by using a special version of the righthand grip rule (Figure 4.1.10). In this situation, you must curl your fingers in

the direction of the conventional current around the solenoid and your thumb

will point in the direction of the magnetic field. Your thumb will point to the

end of the solenoid that forms a north pole. A coil such as this is used to make

an electromagnet or simply to produce a magnetic field.



(b)



Figure 4.1.9 (a) The right-hand grip rule

can be used for a current loop.

(b) Magnetic field lines around

a single wire loop



N



S



Figure 4.1.10 The right-hand grip rule is

used to find the direction of

the magnetic field inside the

solenoid.



The North Pole?



D



id you know that the

Earth’s north geographic

pole is actually its south

magnetic pole? The north pole

of a magnet is attracted towards

the north geographic pole and

therefore it must be a south

magnetic pole. Did you also

know that the Earth’s magnetic

field changes direction? At

irregular intervals of about

250 000 years the polarity of

the Earth’s magnetic field flips

and points in the opposite

direction. Scientists are not

sure of the effects of this flip

or for how long the field

disappears during each flip.



Geographic

North Pole



Magnetic

South Pole



S



N



Magnetic

North Pole



Geographic

South Pole



Figure 4.1.11 The Earth acts as though it has a south magnetic pole near the geographic

north pole! The ‘magnetic north pole’ is the place to which the north end of

a compass appears to point.



88



motors and

generators



Checkpoint 4.1



1 Define the nature and direction of conventional direct current.

2 Construct two-dimensional diagrams illustrating the magnetic field around a current-carrying wire from two

different perspectives (end-on and side-on).

3 Sketch and compare two diagrams illustrating the magnetic field around a bar magnet and a current-carrying

solenoid.



4.2 Forces on charged particles

in magnetic fields

We have already seen that free charged particles move when placed in an electric

field, because they experience a force (Figure 4.1.1). This force is caused by the

attraction and repulsion that charged particles experience within the field.

Knowing why this occurs, it might seem strange to hear that a charged particle

also experiences a force due to a magnetic field. There is, however, one important

A charged particle only experiences a force in a magnetic field

difference.

when the particle is moving relative to the magnetic field, or if the strength of

the magnetic field is changing. It is important to know that stationary charges or

charges moving parallel to the magnetic field do not experience a force.

In Figure 4.2.1a, a positively charged particle, let’s say a proton of charge q,

is travelling upwards with a velocity v within a horizontal magnetic field B. The

proton experiences a force F in a direction perpendicular to both the magnetic

field and the direction in which it is moving. The force is given by F = qvB. The

way we can tell the direction in which the force is acting is to introduce another

right-hand rule. This rule is commonly called the right-hand palm

a

rule (or the right-hand push rule) and is illustrated in Figure 4.2.1b.

To find the direction of the force that a positive particle will

experience when moving through a perpendicular magnetic field:

1 Place your open right hand with the fingers pointing in the

direction of the magnetic field (north to south).

2 Place your thumb at right angles to your fingers and in the

direction in which the particle is travelling.

b

3 The force on the positive particle will be directed out of your

palm and at right angles to your hand.

We can conclude that the proton in Figure 4.2.1a will experience

a force out of the page at right angles to both the magnetic field and

the direction in which the proton is travelling. Note that if we know

the direction of any two of the three quantities represented in the

right-hand palm rule, we can use this rule to determine the direction

of the third quantity.



v

B

S



+



N



F



direction in which the

particle is travelling

with velocity v



B

direction of the

magnetic field

direction of the force F

on the positive particle



Figure 4.2.1 The right-hand palm rule is used

to find the direction of a force

acting on a positively charged

particle in a magnetic field.



89



4



Electrodynamics:

moving charges

and magnetic fields



Try this!

Bending beams of particles

Ask your teacher if they can show you a beam of electrons

in a Crookes magnetic deflection tube (see Figure 4.2.2).

With teacher supervision, bring the north pole of a magnet

close to the front of the tube and observe the effect on the

beam of electrons. By the right-hand palm rule, negative

particles experience a force out of the back of your hand.

Try to predict the direction in which electrons will be

deflected when you place the south pole of the magnet

close to the front of the tube. Now try it and then explain

it to a friend. Do they agree with your explanation?



Figure 4.2.2 A Crookes magnetic deflection tube

produces a beam of electrons.



Checkpoint 4.2

1 Explain why a stationary charged particle experiences a force when you move a magnet past it.

2 Identify the direction in which the proton in Figure 4.2.1a would be moving for it to experience a force into the page.



4.3 The motor effect



Identify that the motor effect

is due to the force acting on

a current-carrying conductor

in a magnetic field.



PRACTICAL

EXPERIENCES

Activity 4.1



Activity Manual, Page

27



90



In the previous section we saw that charges moving in a magnetic field

If a current-carrying conductor is placed in an external

experience a force.

magnetic field, the wire also experiences a force and this is called the motor

effect. This effect occurs because the charges within the wire are travelling

through the magnetic field and experience a force, just as they would if they were

Remember, we are considering

free charged particles (see Figure 4.2.1a).

current to be a flow of positive particles. It is actually the negative electrons

that experience the force from the magnetic field. It works just fine to use

conventional current and consider the force is acting on positive particles to keep

things simple.

We can now use the right-hand palm rule we saw in section 4.2 to work out

the direction of the force on a current-carrying wire in an external magnetic field

To find the direction of the force that acts on a current(see Figure 4.3.1).

carrying wire that is perpendicular to an external magnetic field:

1 Place your open right hand with the fingers pointing in the direction of the

magnetic field (north to south).

2 Place your thumb at right angles to your fingers and in the direction in which

the conventional current is flowing (from the positive to negative terminals

in the circuit).

3 The force experienced by the wire will be directed out of your palm at right

angles to your hand.