7.16 Magnetic Force on a Current-Carrying Conductor

• A current-carrying conductor produces its own magnetic field
  • An external magnetic field will therefore exert a magnetic force on it

• A current-carrying conductor (eg. a wire) will experience the maximum magnetic force if the current through it is perpendicular to the direction of the magnetic flux lines
  • A simple situation would be a copper rod placed within a uniform magnetic field
  • When current is passed through the copper rod, it experiences a force which makes it accelerate

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

• The force F on a conductor carrying current I in a magnetic field with flux density B is defined by the equation

F = BIL sin θ

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

• This equation shows that the magnitude of the magnetic force F is proportional to:
  • Current I 
  • Magnetic flux density B
  • Length of conductor in the field L
  • The sine of the angle θ between the conductor and the magnetic flux lines

Magnitude of the force on a current carrying conductor depends on the angle of the conductor to the external B field

• The maximum force occurs when sin θ = 1
  • This means θ = 90^o and the conductor is perpendicular to the B field
  • This equation for the magnetic force now becomes:

F = BIL

• The minimum force (0) is when sin θ = 0
  • This means θ = 0^o 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

Step 1: Write down the known quantities

• • Magnetic flux density, B = 80 mT = 80 × 10^-3 T
  • Current, I = 0.87 A
  • Length of wire, L = 1.4 m
  • Angle between the wire and the magnetic flux lines, θ = 30^o

Step 2: Write down the equation for the magnetic force on a current-carrying conductor

F = BIL sin θ

Step 3: Substitute in values and calculate

F = (80 × 10^-3) × (0.87) × (1.4) × sin (30) = 0.04872 = 0.049 N (2 s.f)

• Fleming's Left Hand Rule was previously used to determine the direction of the magnetic force on a moving charged particle in a magnetic field
• It can also be used to determine the direction of the magnetic force on a current-carrying conductor in a magnetic field
  • This is because inside a conductor (e.g. a wire) there are many charged particles flowing as a current

• As a reminder, the image representing Fleming's Left Hand Rule is shown below: 

Fleming's Left Hand Rule. Remember, current is the flow of conventional current (i.e. positive to negative)

• Using the conventional symbols representing vectors like magnetic flux density B and force F that go into the page (arrows) or out of the page (dots) we can apply Fleming's Left Hand Rule to problems in 3D

Step 1: Apply the instructions for Fleming's Left Hand Rule

• • Using Fleming’s Left Hand Rule for the quantities given:

First finger is the magnetic field, B = into the page (or screen!)

Thumb is the direction of the magnetic force F = vertically downwards

Step 2: Determine the direction of the conventional current

• • The first finger should be pointing into the page (or screen!) along the direction of the field
  • Rotating the entire hand allows the thumb to point downwards, along the direction of force
  • The second finger should be pointing towards the left of the page (or screen!)
  • This is the direction of conventional current in the wire, i.e., from right to left