Magnetic Force on a Current-Carrying Conductor (HL IB Physics)

• A current-carrying conductor produces its own magnetic field
  • When interacting with an external magnetic field, it will experience a force

• The force F on a conductor carrying current I at an angle θ to a magnetic field with flux density B is defined by the equation

• Where:
  • F = force on a current-carrying conductor in a B field (N)
  • B = magnetic flux density of applied B field (T)
  • I = current in the conductor (A)
  • L = length of the conductor (m)
  • θ = angle between the conductor and applied B field (degrees)

• This equation shows that the force on the conductor can be increased by:
  • Increasing the strength of the magnetic field
  • Increasing the current flowing through the conductor
  • Increasing the length of the conductor in the field

• Note: The length L represents the length of the conductor that is within the field

The magnitude of the force on a current-carrying conductor depends on the angle of the conductor to the external B field

• A current-carrying conductor (e.g. a wire) will experience the maximum magnetic force if the current through it is perpendicular to the direction of the magnetic field lines
  • It experiences no force if it is parallel to magnetic field lines

• The maximum force occurs when sin θ = 1
  • This means θ = 90° and the conductor is perpendicular to the B field

• The equation for the magnetic force becomes:

• The minimum force, i.e. F = 0 N, is when sin θ = 0°
  • This means θ = 0° and the conductor is parallel to the B field

• It is important to note that a current-carrying conductor will experience no force if the current in the conductor is parallel to the field
  • This is because the F, B and I must be perpendicular to each other

Observing the Force on a Current-Carrying Conductor

• The force due to a magnetic field can be observed by
  • placing a copper rod in a uniform magnetic field
  • connecting the copper rod to a circuit

• When current is passed through the copper rod, it experiences a force
  • This causes it to accelerate in the direction of the force

A copper rod moves within a magnetic field when current is passed through it

• When a current-carrying conductor is placed in a magnetic field, the force, B-field and current are all mutually perpendicular to each other
  • Their directions can be determined using Fleming’s left-hand rule

• To use Fleming's left-hand rule, point the thumb, first finger and second finger at right angles to each other
  • The thumb points in the direction of motion or force F of the conductor
  • The first finger points in the direction of the applied magnetic field B
  • The second finger points in the direction of the flow of conventional current I (from positive to negative)

Fleming's Left-Hand Rule

Fleming’s left-hand rule allows us to visualise the 3D arrangement of the force, magnetic field and current

Representing Magnetic Fields in 3D

• When solving problems in three-dimensional space, the current, force or magnetic field could be directed into or out of the page
• When the magnetic field is directed into or out of the page, the following symbols are used:
  • Dots (sometimes with a circle around them) represent the magnetic field directed out of the plane of the page
  • Crosses represent the magnetic field directed into the plane of the page

When the magnetic field is directed into or out of the page, we represent this with crosses or dots, respectively

• The way to remember this is by imagining an arrow used in archery or darts:
  • If the arrow is approaching head-on, such as out of a page, only the very tip of the arrow can be seen (a dot)
  • When the arrow is receding away, such as into a page, only the cross of the feathers at the back can be seen (a cross)