Effects of magnetic fields

A magnetic field is the effect we can see from the movement of charges or from magnets. A moving charge will experience a force in a magnetic field. For more information on these fields, click here.

Use this page to revise the following concepts within effects of magnetic fields:

Magnetic force on a point charge

Charged particles will only experience a force in a magnetic field if they are moving. The direction of the force is both perpendicular to the direction of the magnetic field and the direction of the particle’s velocity .

The force is given by:

\[ F = qvB\sin(\theta) \]

Where:

  • \(F\) = magnetic force on the point charge \((\mathrm{N})\)
  • \(q\) = charge of the point charge \((\mathrm{C})\)
  • \(v\) = speed of the charge \((\mathrm{ms}^{-1})\)
  • \(B\) = magnetic field strength \((\mathrm{T})\)
  • \(\theta\) = angle between the velocity and the magnetic field

If the magnetic field is parallel to the velocity, \(\sin(\theta) = 0\) and there is no force. If the magnetic field is perpendicular to the velocity, \(\sin(\theta) = 1\) and the force is at a maximum.

The direction of the force is found by using the right-hand palm rule:

  • The thumb points in the direction of the positive charge
  • The fingers point on the direction of the magnetic field
  • The palm points in the direction of the force experienced by the charge in the magnetic field.

An open right-hand shows the application of the right-hand palm rule. An arrow from the thumb pointing upwards represents direction of positive charge movement. An arrow pointing left originates from the extended fingers to represent the direction of the magnetic field. An arrow pointing out-of-page away from the palm represents the direction of positive force on positive charge

Note

It is important to note that this is for a positive charge When dealing with a negative charge either:

  • Reverse the thumb direction before applying the right-hand palm rule or.
  • Apply the right-hand palm rule and reverse the direction of the force.

Worked Example

A proton enters a magnetic field \((B = 4 \times 10^{-3} \mathrm{~T})\) at a speed of \(2.5 \times 10^6 \mathrm{~ms}^{-1}\). Determine the magnitude of the force on the proton as it enters the field.

A positively-charged particle with velocity, v, moves to the right, into a magnetic field with field lines directed into the page.

To calculate the magnitude:

\[ F = qvB = (1.6 \times 10^{-19})(2.5 \times 10^6)(4 \times 10^{-3}) = 1.6 \times 10^{-15} \mathrm{~N} \]

  • The direction of the magnetic field is into the page.
  • The direction of the proton’s velocity is to the right.
  • Hence, using the right-hand palm rule, the direction of the force is up.

The magnetic force on an electric charge is always perpendicular to the motion of the charge. This results in the charge moving in a circle, as seen in the diagram below:

A diagram shows the motion of a charged particle (-q) in a magnetic field, B-sub-in, directed into the page. The particle moves in a circular path due to the magnetic forc, F, which is perpendicular to its velocity, v, at every point, maintaining the circular trajectory.

By equating the equations for magnetic force \((F = qvB)\) and force due to circular motion \((F = \frac{mn^2}{r})\) we get:

\[
qvB = \frac{mv^2}{r}
\]
\[
r = \frac{mv}{qB}
\]

and the radius of the circular motion can be found.

Magnetic force on a current-carrying wire

A wire carrying current is essentially a stream of charged particles moving in the same direction. It can be shown that the equation for magnetic force on a point charge can be generalised to become:

Magnetic force on a current-carrying wire

\[ F = IlB \]

Where:

  • \(F\) = magnetic force on the wire \((\mathrm{N})\)
  • \(I\) = current in the wire \((\mathrm{A})\)
  • \(l\) = length of wire in the magnetic field \((\mathrm{m})\)
  • \(B\) = magnetic field strength \((\mathrm{T})\)