A wire carries a constant current of I = 2 A and is placed in a constantmagnetic field  B = (9i − 6j − 14k) T. Determine the magnitude of the force on the segment of the wire that...

A wire carries a constant current of I = 2 A and is placed in a constant
magnetic field  B = (9i − 6j − 14k) T.

Determine the magnitude of the force on the segment of the wire that extends
from the point (2, 4, 18) to the point (11, 1, 2). Assume all positions
are measured in meters.

justaguide | Certified Educator

A wire carries a constant current of I = 2 A and is placed in a constant
magnetic field  B = (9i - 6j - 14k) T.

If a wire through which the flow of current is represented by the vector bar I, is placed in a magnetic field bar B, the force on length L is given by F = `bar I *L ox bar B` .

Here, `bar B = (9i- 6j- 14k)` , I = 2 and `bar L = 9i - 3j - 16k` .

The force F = `2*(9i - 3j - 16k) ox (9i - 6j - 14k)`

= -108i - 36j - 54k

The magnitude of the force is the magnitude of the vector -108i - 36j - 54k, which is equal to 126 N.