AQA A Level Physics复习笔记7.8.1 Magnetic Force on a Current-Carrying Conductor

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

   

• 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 field lines
  • It experiences no force if it is parallel to magnetic field 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 strength of a magnetic field is known as the magnetic flux density, B
  • This is also known as the magnetic field strength
  • It is measured in units of Tesla (T)

   

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

F = BIL sinθ

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

   

• This equation shows that the greater the current or the magnetic field strength, the greater the force on the conductor
• The length of the conductor, L in this equation is only the length that is within the field

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
  • This is because the F, B and I must be perpendicular to each other

   

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 field, θ = 30o

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

F = BIL sinθ

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)