6.3.1 Magnetic fields

A magnetic field is a field surrounding a permanent magnet or a current carrying conductor in which magnetic objects experience a force. We can detect the presence of a magnetic field using a plotting compass/iron fillings. Magnetic field lines/lines of force map magnetic field patterns around current-carrying wires/magnets:

• The arrow on the magnetic field line shows the direction in which a free north pole would move
• Equally spaced parallel magnetic field lines represent a uniform field (the strength does not vary)
• The magnetic field is stronger when the magnetic field lines are closer.
• Like poles repel and unlike/different poles attract

NOTE: with iron fillings, the field induces magnetism in the filings which line up in the field.

When a wire carries a current a magnetic field is created around the wire. The field is created by the electrons moving within the wire. Any moving charged particle creates a magnetic field in the space around it. The electric field of a bar magnet is created by the electrons whizzing around the iron nuclei.

For a current-carrying wire the magnetic field lines are concentric circles centred on the wire and perpendicular to it. The direction of the magnetic field can be determined using the right hand grip (thumb points in direction of conventional current, direction of the field is given by the direction the fingers curl). Coils and solenoids both produce north and south poles. At the centre of the solenoid the magnetic field is uniform.


When a current-carrying wire/conductor is placed in an external magnetic field the two fields interact just like the fields of a permanent magnet. The direction of force experienced by a current carrying wire placed perpendicular to the external magnetic field can be determined using Fleming's left-hand rule.  The first finger gives the direction of the external magnetic field, the second finger gives the direction of motion of the conventional current, and the thumb gives the direction of motion of the wire:

Magnetic flux density
The magnetic force experienced by a wire in an external magnetic field depends on a number of factors (e.g force is a maximum when the wire is perpendicular to the field and zero when parallel. The magnitude of the force (F) experienced by the wire is directly proportional to:

• the current 'I'
• the length 'L' of the wire in the magnetic field
• sinθ (θ is the angle between the magnetic field and the current direction
• the strength of the magnetic field

From these observations we can form the equation:

F = B I L sinθ

B is the magnetic flux density (the strength of the field). The SI unit for magnetic flux density is the tesla (T). 1 T = 1 N m^-1 A^-1. The magnetic flux density is 1 T when a wire carrying a current of 1 A placed perpendicular to the magnetic field experiences a force of 1 N per metre of its length. 

When the wire is perpendicular to the magnetic field θ=90. Sin 90 = 1 so F = B I L. This means the equation for magnetic flux density can be written as:

B = F / (I L)

We need to know as experiment to determine the uniform magnetic flux density between poles of a magnet using a current-carrying wire and digital balance:

• Place two bar magnets on top of a balance
• Hold a stiff copper wire between them perpendicular to the magnetic field between the two poles
• measure the length L of the wire in the field using a ruler
• connect the wire in series with an ammeter and variable power supply using crocodile clips
• Zero the balance when there is no current in the wire
• When there is a current I flowing through the circuit, the wire experiences a vertical upward force (Fleming's left hand rule). According to N3 the magnets experience an equal downward force. This force can be calculated from the change in mass reading using F = mg.
• The magnetic flux density can be determined from B = F/(IL)

Image credit: Kerboodle OCR A physics textbook