• 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 = 90o?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 = 0o?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?= 30o

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