Question

A hypothetical magnetic field existing in a region is given by →B=B0→er, where →er denotes the unit vector along the radial direction. A circular loop of radius a, carrying a current i, is placed with its plane parallel to the x−y plane and the centre at (0, 0, d). Find the magnitude of the magnetic force acting on the loop.

Answer 1

To Find: The magnitude of the magnetic force acting on the loop.

Explanation:

Given:

In a region, an existing hypothetical magnetic field,

B→ = B0e→r

Where e→r along the radial direction, signifies the unit vector.

Radius of a circular loop is a

So, the loop’s length, l = 2πa

Electric current flowing via loop = i

According to the information provided, the loop is positioned with its centre and its parallel plane to the X−Y plane is at (0, 0, d).

Now, the angle between the magnetic field and the length of the loop is θ.

Magnetic force is shown as

F →= il→×B→F →

= i 2πa ×B→F→ = i 2πB0 a2 a2+d2