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 will only experience a force if the current through it is perpendicular to the direction of the 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 that makes it move
A copper rod moves within a magnetic field when current is passed through it
Calculating Magnetic Force on a Current-Carrying Conductor
- 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 magnetic field (N)
- B = magnetic flux density of external magnetic field (T)
- I = current in the conductor (A)
- L = length of the conductor (m)
- θ = angle between the conductor and external magnetic field (degrees)
- This equation shows that the greater the current or the magnetic field strength, the greater the force on the conductor
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
Worked example
A current of 0.87 A flows in a wire of length 1.4 m placed at 30o to a magnetic field of flux density 80 mT.
Calculate the force on the wire.
Answer:
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)
Exam Tip
Remember that the direction of current flow is the flow of positive charge (positive to negative), and this is in the opposite direction to the flow of electrons