How do you calculate the force on a current-carrying conductor?

To calculate the force on a current-carrying conductor, use the formula F = BIL sin(θ).

When a conductor carrying an electric current is placed in a magnetic field, it experiences a force. This force can be calculated using the formula F = BIL sin(θ), where F is the force in newtons (N), B is the magnetic flux density in teslas (T), I is the current in amperes (A), L is the length of the conductor in the magnetic field in metres (m), and θ is the angle between the direction of the current and the magnetic field.

The magnetic flux density, B, represents the strength of the magnetic field. The current, I, is the flow of electric charge through the conductor. The length, L, is the part of the conductor that is within the magnetic field. The angle, θ, is crucial because the force depends on the orientation of the conductor relative to the magnetic field. When the conductor is perpendicular to the magnetic field (θ = 90°), sin(θ) is 1, and the force is maximised. If the conductor is parallel to the magnetic field (θ = 0°), sin(θ) is 0, and the force is zero.

For example, if you have a wire of length 0.5 metres carrying a current of 3 amperes, placed in a magnetic field of 0.2 teslas at an angle of 90 degrees to the field, the force can be calculated as follows: F = 0.2 T * 3 A * 0.5 m * sin(90°). Since sin(90°) is 1, the force F = 0.2 * 3 * 0.5 * 1 = 0.3 newtons.

Understanding this concept is essential in many practical applications, such as electric motors and generators, where the interaction between current and magnetic fields is used to produce motion or electricity.