AP Physics 2 Exam Question:

A wire of length 0.5 m is carrying a current of 2 A along the positive x-direction. A magnetic field with a magnitude of 0.25 T is directed along the positive y-direction. Find the magnetic force experienced by the wire and determine the direction of the force.

Answer:

The magnetic force experienced by a wire carrying a current in a magnetic field is given by the formula:

F = I * L * B * sin(θ)

Where:

• F is the magnetic force (in Newtons),
• I is the current (in Amperes),
• L is the length of the wire (in meters),
• B is the magnetic field strength (in Tesla),
• θ is the angle between the wire and the magnetic field.

Here, the current (I) = 2 A, the length of the wire (L) = 0.5 m, and the magnetic field (B) = 0.25 T. As the wire is perpendicular to the magnetic field, the angle (θ) = 90 degrees.

Substituting the given values into the formula:

F = (2 A) * (0.5 m) * (0.25 T) * sin(90°)

Simplifying the equation:

F = (2 A) * (0.5 m) * (0.25 T) * 1

F = 0.25 N

Therefore, the magnetic force experienced by the wire is 0.25 N.

The direction of the force can be determined using the right-hand rule. When the index finger points in the direction of the current (positive x-direction), and the middle finger points in the direction of the magnetic field (positive y-direction), the thumb will point in the direction of the magnetic force. Thus, the magnetic force is directed along the negative z-direction.

Therefore, the magnetic force experienced by the wire is 0.25 N, directed along the negative z-direction.