Example 4.10 Explanation

The horizontal component of the earth's magnetic field at a certain place is \(3.0 \times 10^{-5} \, \text{T}\) and the direction of the field is from the geographic south to the geographic north. A very long straight conductor is carrying a steady current of 1A.

The force per unit length on a current-carrying conductor in a magnetic field is given by:

F = I × B or F = IB sinθ

Where:

• F is the force on the conductor
• I is the current (1A in this example)
• B is the magnetic field strength (\(3.0 \times 10^{-5} \, \text{T}\))
• θ is the angle between current direction and magnetic field direction

Key observations from this example:

• When current flows east-west (θ = 90°), the force is maximum: \(3 \times 10^{-5} \, \text{N/m}\) downward
• When current flows south-north (θ = 0°), there is no force (sin0° = 0)