Question

A magnetic field is used to suspend a wire of mass 0.045 kg and length 0.22 m. The wire is carrying a current of 11.0 A. Calculate the magnitude of the minimum magnetic-field strength that is needed to balance the gravitational force.

Answer 1

To balance the gravitational force acting on the wire, the minimum magnetic-field strength needed is approximately 0.180 T.

Step-by-step explanation:

The gravitational force acting on the wire can be calculated using the formula:

Fg = mg

where Fg is the gravitational force, m is the mass of the wire, and g is the acceleration due to gravity.

The magnetic force acting on the wire can be calculated using the formula:

Fm = BIL

where Fm is the magnetic force, B is the magnetic field strength, I is the current in the wire, and L is the length of the wire.

In order to balance the gravitational force, the magnetic force must be equal in magnitude. Therefore, we can set Fg = Fm and solve for B:

B = mg / (IL)

Substituting the given values into the formula, we get:

B = (0.045 kg * 9.8 m/s^2) / (11.0 A * 0.22 m)

Solving this equation yields a magnetic field strength of approximately 0.180 T.