A wire carrying of 3 Amper current around a non conducting cube of side 1 metre.find magnitude of magnetic moment due to wire will be

To find the magnetic moment due to a wire carrying a current around a non-conducting cube, we can use the concept of magnetic moment in relation to current loops. The magnetic moment (μ) is a vector quantity that represents the strength and direction of a magnetic source. In this case, the wire forms a closed loop around the cube, and we can treat it as a series of current loops. Let's break down the calculation step by step.

Understanding the Setup

We have a wire carrying a current of 3 Amperes (A) that wraps around a cube with a side length of 1 meter. The wire essentially forms a closed loop around the cube. The magnetic moment can be calculated using the formula:

Magnetic Moment Formula

The magnetic moment (μ) for a current loop is given by:

μ = I × A

• I is the current in Amperes.
• A is the area of the loop in square meters.

Calculating the Area of the Loop

Since the wire is wrapped around a cube, we need to determine the effective area that the current loop encloses. For a cube, if we consider the wire to be wrapping around the edges, we can visualize it as forming a square loop on each face of the cube.

The area of one face of the cube is:

A = side × side = 1 m × 1 m = 1 m²

Considering the Total Current Loops

However, the wire wraps around all six faces of the cube. Since the wire effectively creates a loop around each face, we can consider the contribution of each face. The total area enclosed by the wire can be thought of as the sum of the areas of the loops formed around each face. But since the wire wraps around the cube, we can simplify our calculation by considering the wire as forming a single effective loop around the cube.

Calculating the Magnetic Moment

Now, substituting the values into the magnetic moment formula:

μ = I × A = 3 A × 1 m² = 3 A·m²

Final Result

The magnitude of the magnetic moment due to the wire carrying a 3 Ampere current around the non-conducting cube is:

μ = 3 A·m²

This result indicates the strength of the magnetic field generated by the current loop around the cube, which can be significant in applications involving magnetic fields and forces. Understanding this concept is crucial in fields such as electromagnetism and electrical engineering.