Wire with Current in Magnetic Field

Use equation $F=I\ell B\sin \theta$ to find the magnitude of the force on the wire. The length of the wire inside the magnetic field is 4.0 cm, and the angle between the current direction and the magnetic field direction is 90°. To find the direction of the force, use the right-hand rule as explained just after the equation $F=I\ell B\sin \theta \text{.}$

Insert the given values into equation $F=I\ell B\sin \theta$ to find the magnitude of the force

To find the direction of the force, begin by placing the current vector end to end with a vector for the magnetic field. The result is as shown in the figure in the previous Worked Example with $\overrightarrow{v}$ replaced by $\overrightarrow{I}$ . Curl your right-hand fingers from $\overrightarrow{I}$ to $\overrightarrow{B}$ and your right thumb points down the page, again as shown in the figure in the previous Worked Example. Thus, the direction of the force is in the $\widehat{x}$ -direction. The complete force is thus $\left(0.12\text{N}\right)\widehat{x}$ .