## Understanding The Torque Expression Of A Current-Carrying Conductor

# Understanding the Torque Expression of a Current-Carrying Conductor

When a conductor carries an electric current, the torque expression of the conductor can be calculated by understanding the magnetic force that acts on it. This article will explain the torque expression of a current-carrying conductor in detail.

## What Is a Torque Expression?

A torque expression is a mathematical equation that describes the relationship between the force exerted on an object and its rotational motion. It is calculated by multiplying the magnitude of the force, the distance between the force and the axis of rotation, and the sine of the angle between the two.

## Understanding the Magnetic Force

When an electric current flows through a conductor, it produces a magnetic field around it. This magnetic field exerts a force on the current-carrying conductor, which increases with the current and the length of the conductor. This force is known as the Lorentz force, and is the basis for calculating the torque expression of a current-carrying conductor.

## Calculating the Torque Expression

The torque expression of a current-carrying conductor can be calculated using the following equation:

**T = μ × I × L × sin θ**

Where **T** is the torque, **μ** is the magnetic permeability of the conductor material, **I** is the current, **L** is the length of the conductor, and **θ** is the angle between the current and the axis of rotation.

## Example Calculation

Let's say we have a current-carrying conductor with a length of 5 cm, a current of 3 A, and a material with a magnetic permeability of 4. We also know that the angle between the current and the axis of rotation is 45 degrees. We can calculate the torque expression of this conductor using the equation above:

**T = μ × I × L × sin θ**

**T = 4 × 3 × 5 × sin (45) = 60 Nm**

## Conclusion

The torque expression of a current-carrying conductor can be calculated using the equation **T = μ × I × L × sin θ**, where **μ** is the magnetic permeability of the conductor material, **I** is the current, **L** is the length of the conductor, and **θ** is the angle between the current and the axis of rotation. By understanding the force acting on a current-carrying conductor, we can calculate the torque expression and understand the effect of the current on its rotational motion.