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
- 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
Magnetic force on a current-carrying 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:
- 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
Step 3: Substitute in values and calculate
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