Question:

A wire carrying a current of 5 A is placed in a uniform magnetic field of 0.2 T. The wire is oriented perpendicular to the magnetic field. The length of the wire is 2 m. Calculate the magnetic force experienced by the wire.

(a) Calculate the magnitude of the magnetic force on the wire.
(b) Determine the direction of the magnetic force on the wire.

Assume the wire is a straight conductor and ignore any interactions between segments of the wire.

Answer:

(a) To calculate the magnitude of the magnetic force on the wire, we can use the following formula:

Where:

• $I$ is the current flowing through the wire,
• $L$ is the length of the wire,
• $B$ is the magnitude of the magnetic field, and
• $\theta$ is the angle between the wire and the magnetic field.

In this case, the wire is perpendicular to the magnetic field, so $\theta = 90^\circ$ and $\sin(\theta) = 1$. Substituting the given values:

Therefore, the magnitude of the magnetic force on the wire is 2 N.

(b) To determine the direction of the magnetic force on the wire, we can use the right-hand rule. The right-hand rule states that if you point your right thumb in the direction of the conventional current (opposite to the electron flow), and then curl your fingers, the direction in which your fingers curl represents the direction of the magnetic field lines.

In this case, if we point our right thumb in the direction of the current flow with our fingers curled in the direction of the magnetic field, our palm will point in the direction of the magnetic force on the wire. Since the wire is perpendicular to the magnetic field, the force will be either into or out of the plane of the page.

Hence, the direction of the magnetic force is normal to the plane of the wire (either into or out of the page).