Magnetic fields and forcesEdexcel A-Level Physics: Revision notes

A magnetic field exerts a force on moving charges and on current-carrying conductors. The strength of the field is described by the magnetic flux density $B$, measured in tesla (T). Field lines show its direction: the closer the lines, the stronger the field.

One tesla is the flux density that produces a force of 1 N on a 1 m length of conductor carrying a current of 1 A at right angles to the field, so $1\ \text{T} = 1\ \text{N A}^{-1}\text{m}^{-1}$.

A field is uniform if the flux density has the same size and direction at every point, for example between two flat parallel pole pieces.

A conductor carrying a current in a magnetic field experiences a force given by

$F = BIl\sin\theta$

where $\theta$ is the angle between the current direction and the field, $I$ is the current and $l$ is the length of conductor in the field.

• At $\theta = 90^\circ$ the force is a maximum, $F = BIl$.
• At $\theta = 0^\circ$ (current parallel to the field) the force is zero.

Worked example. A 0.12 m wire carries 5.0 A at 30° to a 0.30 T field. $F = 0.30 \times 5.0 \times 0.12 \times \sin 30^\circ = 0.090\ \text{N}$.

The direction of the force is given by Fleming's left-hand rule. Hold the thumb, first finger and second finger of the left hand at right angles:

• First finger: the direction of the magnetic Field (north to south)
• SeCond finger: the direction of the conventional Current (positive to negative)
• Thumb: the direction of the Thrust (force) or motion

The force is always perpendicular to both the current and the field. Reversing either the current or the field reverses the force; reversing both leaves it unchanged.

A single charge $Q$ moving with speed $v$ at an angle $\theta$ to a field experiences

$F = BQv\sin\theta$

This is the same effect as $F = BIl\sin\theta$, since a current is a flow of moving charges.

• The force is perpendicular to the velocity, so it changes the direction of motion but does no work and does not change the speed.
• There is no force on a charge moving parallel to the field, or on a stationary charge.
• For a negative charge, such as an electron, the force is in the opposite direction to that on a positive charge moving the same way.

Worked example. A proton moving at $2.4\times10^{6}$ m s⁻¹ at right angles to a 0.050 T field: $F = 0.050 \times 1.60\times10^{-19} \times 2.4\times10^{6} = 1.9\times10^{-14}$ N.

The magnetic flux $\Phi$ through an area $A$ perpendicular to a uniform field is

$\Phi = BA$

measured in weber (Wb), where $1\ \text{Wb} = 1\ \text{T m}^2$. If the normal to the area makes an angle $\theta$ with the field, then $\Phi = BA\cos\theta$, because only the component of the field perpendicular to the area counts. The flux is zero when the plane is parallel to the field.

For a coil of $N$ turns the flux linkage is

$N\Phi = BAN\cos\theta$

in Wb (turns).

Worked example. A 250-turn coil of area $4.0\times10^{-3}$ m² with its plane perpendicular to a 0.18 T field: $\Phi = 7.2\times10^{-4}$ Wb and $N\Phi = 0.18$ Wb (turns). Tilting it so the normal is at 60° halves this to 0.090 Wb (turns).