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Magnetic Force

Physics: IB Diploma Higher Level, topic 4.6.3

Magnetic Force

Magnetic force is the attractive or repulsive force felt by a charge when it is moving in a magnetic field.

Magnetic force

Magnetic force

  • The magnetic force vector can be calculated using the following equation:
  • FM→=q(v→×B→)\overrightarrow{F_M}=q (\overrightarrow{v}\times \overrightarrow{B})
  • The magnitude of the magnetic force is then:
  • ∣FM→∣=∣qv→∣sin⁡θ∣B→∣|\overrightarrow{F_M}|=|q\overrightarrow{v}|\sin{\theta}| \overrightarrow{B}|
  • Where θ{\theta} is the angle between the velocity and the field lines.
Magnetic field strength

Magnetic field strength

  • The magnetic field strength, B→\overrightarrow{B}, is a measure of how dense the field lines are.
  • The units of magnetic field strength are Tesla (T).

Force on a charged particle

A magnetic field will create a force on a charged particle. This is called the Lorentz force.

Lorentz force

Lorentz force

  • The Lorentz force always acts perpendicular to the velocity of a particle.
  • This means that the force acts as a centripetal force.
  • Particles in magnetic fields undergo circular motion.
Calculation

Calculation

  • We know that the centripetal force is given by
  • Fc→=m∣v→∣2/r\overrightarrow{F_c}=m| \overrightarrow{v}|^2/r
  • If the particle is traveling in a magnetic field perpendicular to the field lines it must be acted upon by the Lorentz force
  • ∣FM→=q∣v→∣∣B→∣| \overrightarrow{F_M}=q| \overrightarrow{v}|| \overrightarrow{B}|
Calculation 2

Calculation 2

  • If we equate the two forces we get
  • q∣v→∣∣B→∣=m∣v→∣2rq| \overrightarrow{v}|| \overrightarrow{B}|=m\frac{| \overrightarrow{v}|^2}{r}
  • We can then rearrange to get the radius of the circle
  • r=m∣v→∣q∣B→∣r=\large\frac{m| \overrightarrow{v}|}{q| \overrightarrow{B}|}

Fleming's Left-Hand Rule

Fleming's left-hand rule is a useful way of telling which direction the field, the movement of the charge and the current flow in a magnetic field.

Perpendicular directions

Perpendicular directions

  • The field, the movement of the charge and the current have to be in perpendicular directions, so they must all be at 90o to each other.
  • If you hold your left hand as shown in the image:
  • Your thumb represents the direction of movement of the charge.
  • Your first finger represents the field.
  • Your middle finger represents the current.
Method

Method

  • The question will give you two out of three of these quantities.
  • You will need to line up those fingers then see which direction the last one is pointing in.
  • Remember field lines run from the north pole to the south.

Test yourself on Magnetic Force

  • What is the magnetic field strength a measure of?

  • What is the equation for the force felt by a charge moving in a magnetic field?

  • Which statements about magnetic force are correct?

  • In what direction does the Lorentz force act?

  • Particles in a magnetic field undergo what type of motion?

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