Question

Does increasing the current always increase the magnetic force on the wire? is there a case where increasing the current does not increase the magnetic force on the wire? Describe this case.

Please provide detailed explanation, especially with the second question. Thank you!

Answer 1

Suppose a wire carrying current i is in a magnetic field B, then the magnetic force per unit length on the wire is

where theta is the angle between the direction of the current and the magnetic field.

If this angle is not zero, then clearly the force per unit length is proportional to the current and magnetic field and the force increases as you increase either the magnetic field or current. In fact, the force is maximum when the angle, theta is 90 degrees(when the magnetic field and current are perpendicular to each other.)

But if the angle, theta, is zero, which means the magnetic field and current are parallel, then the force is zero

So, now if you increase the current or magnetic field, the force will still remain zero. This is a case where the force doesn't change even on increasing the magnetic field or current.