IGCSE Physics 0625

4.5.4 Force on a Current-Carrying Conductor

This section explores the relationship between a magnetic field and an electric current, leading to the concept of a force acting on a current-carrying conductor placed within a magnetic field. We will recall and apply the right-hand rule to determine the direction of this force.

Key Concepts

• Magnetic Field (B): A region of space where a magnetic force is experienced. Measured in Teslas (T).
• Electric Current (I): The flow of electric charge. Measured in Amperes (A).
• Force (F): A push or pull exerted on an object. Measured in Newtons (N).
• Right-Hand Rule: A mnemonic device used to determine the direction of the force on a current-carrying conductor in a magnetic field.

The Force Equation

The magnitude of the force (F) on a current-carrying conductor in a magnetic field is given by the equation:

$$F = I L B \sin \theta$$

Where:

• I is the current in the conductor (in Amperes).
• L is the length of the conductor within the magnetic field (in meters).
• B is the strength of the magnetic field (in Teslas).
• θ is the angle between the direction of the current and the direction of the magnetic field.

The Right-Hand Rule

The right-hand rule is used to determine the direction of the force. There are a few variations, but the most common one is:

1. Point your thumb in the direction of the current (I).
2. Point your fingers in the direction of the magnetic field (B).
3. Your palm will then point in the direction of the force (F) on the conductor.

If the current and magnetic field are perpendicular (θ = 90°), the force is at its maximum value: $$F = I L B$$

Example Problem

A current of 2 A flows through a straight wire of length 0.5 m placed in a magnetic field of 0.4 T. The current is perpendicular to the magnetic field. Calculate the force on the wire.

Using the formula: $$F = I L B$$

$$F = 2 \text{ A} \times 0.5 \text{ m} \times 0.4 \text{ T} = 0.4 \text{ N}$$

The direction of the force can be determined using the right-hand rule. The force will be perpendicular to both the wire (current direction) and the magnetic field.

Table Summary

Quantity	Symbol	Units
Force on a current-carrying conductor	F	Newtons (N)
Current	I	Amperes (A)
Length of conductor in magnetic field	L	Meters (m)
Magnetic field strength	B	Teslas (T)
Angle between current and magnetic field	θ	Degrees (° or radians)

Understanding the force on a current-carrying conductor is fundamental to many electrical and magnetic applications, including electric motors and actuators.