A 2.0-m wire carries a current of 15 A directed along the positive x axis in a region where the magnetic field is uniform and given by B = (30 − 40 ) mT. What is the resulting magnetic force on the wire?

Question

A 2.0-m wire carries a current of 15 A directed along the positive x axis in a region where the magnetic field is uniform and given by B = (30  − 40  ) mT. What is the resulting magnetic force on the wire?

Quizplus · Accepted Answer

The magnetic force on a current-carrying wire is given by: $F_B = I\ell 	imes B$, where $\ell$ is the length of the wire in the direction of the current. In this case, the current is along the positive $x$ axis, so we want to find the component of the field perpendicular to the wire in that direction. Using the given components of the field, we have:

$B_y = -40	imes 10^{-3} 	ext{ T}$

$F_B = I\ell B_y = (15 	ext{ A})(2.0 	ext{ m})(-40	imes 10^{-3} 	ext{ T}) = -1.2 	ext{ N}$

The force is in the negative $y$ direction, so the answer is B.

A 20-M Wire Carries a Current of 15 a Directed Along