9.3.A - Forces on Conductors


Electromagnetism manifests as both electric fields and magnetic fields. Both fields are simply different aspects of electromagnetism, and hence are intrinsically related. A changing electric field generates a magnetic field and conversely, a changing magnetic field generates an electric field.

Said another way, moving charges generate magnetic fields. A conductor carrying a current (moving charges) will have a radial magnetic field around it and this can be used to create an electromagnet.

A charged particle moving at right angles to magnetic field lines also experiences a force that is proportional to the strength of the magnetic field. If we consider an electrical conductor (such as a wire) to be a series of moving charges, each charge will experience a force creating an overall force on the conductor. A current carrying conductor therefore experiences a force in the presence of a magnetic field and this is known as the motor effect.

In this unit you will learn about:

  • Magnetic fields and how they are produced,
  • Forces on conductors carrying current in a magnetic field, and
  • Forces between parallel current carrying conductors.


Magnetic Fields

Compasses placed around a bar magnet
will point in the direction of the field lines.

The magnetic field is defined as the force and direction experienced by a positive test charge placed at a point in the field. For this reason, field lines point in the direction of the force and indicate direction from the north pole towards the south pole.

The pattern and the direction of a magnetic field can be determined by a compass. The pointer of the compass will always point in the direction of the magnetic field. A compass will always show that field lines leave a north pole and move towards the south pole.

Magnetic fields can be generated around permanent bar magnets and around current carrying conductors. A conductor can also be wound around an iron cylinder to make an electromagnet. Electromagnets are generally preferable to permanent magnets as the field can be switched on and off with the current and can also be increased and decreased as needed.

 

Permanent Magnets

The magnetic field around a permanent
bar magnet.

Some materials are magnetic because of the arrangement and motion of the electrons around the nuclei of their atoms. Such materials are called ferromagnetic materials, the most common of which is iron. Permanent magnets are usually made from iron or one of its alloys. Some other ferromagnetic materials that exhibit easily detectable magnetic properties are nickel, cobalt, gadolinium and their alloys.

Field lines around magnets should:

  • Exit from the north pole and enter the south pole,
  • Leave perpendicular to the surface of the magnet,
  • Never cross, and
  • Be more dense where the field is stronger and less dense where it is weaker.

Current Carrying Conductors

Using the right hand grip rule to determine the direction
of a magnetic field around a current carrying conductor.

A current carrying conductor creates a radial (circular) magnetic field around its length as shown in the diagram on the right. The direction of the magnetic field can be determined using the right hand grip rule. The thumb points in the direction of conventional current in the wire and the fingers point in the direction of the magnetic field around the wire.

The strength of the magnetic field formed by a current carrying conductor depends on the magnitude of the current. A stronger current will produce a stronger magnetic field around the wire.

The strength of the field also depends on distance from the conductor. The field strength decreases as you move further away as shown by the fact that the fields lines are getting less dense. This is why magnetic field strength is sometimes referred to as magnetic flux density (more on this later).

The SI Unit for magnetic field strength is called the tesla (T) and its symbol is B.

Most magnetic fields are much smaller than 1.0 T. The largest fields generated are those in magnetic resonance imaging machines which go up to a maximum of about 5.0 T.

 

Electromagnets

A schematic diagram of an electromagnet. Note the direction of
the current flow and the common direction of all field lines inside
the solenoid.

The magnetic field around a straight wire is not very strong but can be made stronger by coiling the wire around a piece of soft iron. This electromagnet is sometimes called a solenoid. The shape of the magnetic field is the same as a bar magnet. The soft iron inside the coil makes the magnetic field stronger because concentrates the field lines inside the iron and becomes magnetic itself. Soft iron is used because it loses its magnetism as soon as the current stops flowing and acts as temporary magnet. In this way, the electromagnet can be switched on and off by turning the electricity on and off. Steel forms a permanent magnet. If steel was used inside the coil, it would continue as a magnet after the electricity was switched off. It would not be useful as an electromagnet. Permanent magnets are needed for some applications such as simple DC electric motors, generators, loudspeakers and microphones. Electromagnets are used in other applications such as AC induction motors, some DC motors and generators where the magnetic field needs to be varied or have its direction changed readily.

You should note that winding a current carrying conductor in this way produces field lines inside the solenoid that all run in the same direction. This is what creates the external north and south pole of the electromagnet.

The strength of the magnetic field produced by an electromagnet can be increased by:

  • Using a soft iron core
  • Using more turns of wire on the coil.
  • Using a bigger current.

Reversing the direction of the current will reverse the direction of the magnetic field. This can be useful in many applications such as alarm bells and circuit breakers.

 

Force on a Conductor

Production of a force known as the motor effect due to
the interaction of two magnetic fields.

The laws of electromagnetism tell us that electric charges such as protons and electrons will always experience a force when they move in an external magnetic field. This phenomenon is know as the motor effect.

A current carrying conductor contains electrons all moving with a certain velocity towards a positive potential so you would expect the conductor to experience a force, which it does. It is the interaction of the the external magnetic field with the radial magnetic field around the conductor that produces the force.

The motor effect can be simply demonstrated using the equipment shown below. A conducting carbon (graphite) rod placed between the poles of a permanent magnet and laying on two conducting wires. In the first situation, the carbon rod is free to roll and will experience a force causing it to move towards the right. In the second situation, the directrion of the field has been changed with respect to the conductor.

Maximum force (blue arrow) is produced when the conductor is perpendicular to the field lines. In this case the force is to the right, at maximum and perpendicular to the magnetic field.

Changing the orientiation of the field lines with respect to the conductor will change the direction of the force. In this case the force is still at maximum and perpendicular to the field lines, but will now be upwards.

As you have seen above, the force is maximum when the conductor is perpendicular to the field lines. For this reason, you need to be familiar with different ways to visualise conductors in fields. The diagrams in the table below show different ways to visualise different orientations of the conductor in the field. A cross shows current or field lines going into the page. A point shows them coming out of the page. Imagine an arrow with a point coming towards you and when it moves away from you you see the quill (cross) disappearing into the page. If the point or cross is surrounded by a circle, it denotes current in a conductor. Without the circle it denotes magnetic field lines.




Current left to right
Field lines going into page
Conductor perpendicular to field
Force directed upwards


Current left to right
Field lines coming out of page

Conductor perpendicular to field
Force directed downwards


Current bottom left to top right
Field lines coming out of page

Conductor perpendicular to field
Force directed towards bottom right corner


Current coming out of the page
Field lines left to right
Conductor perpendicular to field
Force directed upwards


Current going into the page
Field lines left to right
Conductor perpendicular to field
Force directed downwards


Current bottom left to top right
Field lines left to right
Conductor at an angle θ
to field lines
Force directed into page

Right Hand Palm Rule

The right-hand palm rule is used to find the direction of force on a conductor carrying current in a magnetic field. Follow the rules below:

  • Use your right hand for conventional current
  • Arrange the fingers so they are parallel
  • Arrange the thumb at 90° to the fingers
  • The force comes directly out of the palm of the hand at right angles to the fingers and the thumb
  • The thumb gives the direction of current
  • The other fingers give the direction of magnetic field

If you are working with electron current, you should use your left hand instead.

Check the examples in the table above to ensure you can correctly identify the direction of the forc on the conductor in each case.

While the direction of the force is determined using the right hand palm rule, the magnitude of the force is calculated using the following equation.

Equation - Calculating the Force on a Conductor

F

B

I

L

θ

force on the conductor

magnetic field strength

current

length of conductor in the field

angle between conductor and field lines

newtons (N)

teslas (T)

amps (A)

metres (m)

degrees (°)

You should use this equation when calculating the magnitude of the force on a conductor placed in an external magnetic field.

 

Force Between Two Current Carrying Conductors

Next we consider what happens when two conductors are placed side-by-side in parallel. When current flows, each conductor sits in the magnetic field of the other conductor. This causes each conductor to experience a force due to the magnetic field of the other conductor and they move together or apart depending on the direction of current flow. The diagrams below show how two conductors carrying current in the same direction generate an attractive force on one another If the currents were in opposite directions, the force would be repulsive.

Two conductors of length, l, separated by a distance, d, carrying current in the same direction. The force is attractive but if the currents were in opposite directions, the force would be repulsive. The strength of the force can be calculated using the equation below.

Conductor 1 creates a radial magnetic field moving into the page where Conductor 2 lies. This creates a force on Conductor 2 towards Conductor 1.

Conductor 2 creates a radial magnetic field moving out of the page where Conductor 1 lies. This creates a force on Conductor 1 towards Conductor 2.

 

Equation - Calculating the Force Between Two Parallel Conductors

F/l

k

I1

I2

d

force per unit length between conductors

magnetic force constant

current in conductor 1

current in conductor 2

distance between conductors

newtons per metre (Nm-1)

2.0 x 10-7 (NA-2)

amps (A)

amps (A)

metres (m)

You should use this equation when calculating the magnitude of the force between two parallel current carrying conductors.