Question

A long-rigid wire lies along the x-axis and carries a current of 2.5 A in the positive x-direction. Around the wire is the magnetic field B = (2.0i + 5.0x²j), with x in meters and B in millitesla. Calculate the magnetic force on the segment of wire between x = 2.0 m and x = 4.0 m?

Answer 1

To calculate the magnetic force on the wire segment between x = 2.0 m and x = 4.0 m, use the formula F = I * L * B * sin(theta), where F is the magnetic force, I is the current, L is the length of the wire segment, B is the magnetic field, and theta is the angle between the current and the magnetic field. In this case, the current is 2.5 A, the length is 2.0 m, the magnetic field is (0.002i + 0.005x^2j) T, and the angle is 0 degrees. Plug these values into the formula to find the magnetic force.

Step-by-step explanation:

To calculate the magnetic force on the segment of wire between x = 2.0 m and x = 4.0 m, we can use the formula F = I * L * B * sin(theta), where F is the magnetic force, I is the current, L is the length of the wire segment, B is the magnetic field, and theta is the angle between the current and the magnetic field.

In this case, the current I is 2.5 A, the length L is (4.0 - 2.0) m = 2.0 m, and the magnetic field B is (2.0i + 5.0x^2j) mT = (0.002i + 0.005x^2j) T. The angle theta between the current and the magnetic field is 0 degrees, since they are in the same direction.

So, the magnetic force on the wire segment is:

F = 2.5 A * 2.0 m * (0.002i + 0.005(2.0)^2j) T * sin(0 degrees)

= 0.01i + 0.02j N.