An electromagnet produces a magnetic field of magnitude 1.5...

An electromagnet produces a magnetic field of magnitude 1.5 T throughout a cylindrical region of radius
6.0 cm. A straight wire carrying a current of 25 A passes through the field as shown in the accompanying figure. What is the magnetic force on the wire?

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Key Concepts

Magnetic Force on a Current-Carrying Conductor

This concept states that when a current-carrying conductor is placed within a magnetic field, it experiences a force given by the equation F = I (L × B), where I is the current, L is the length vector of the conductor within the magnetic field, and B is the magnetic field strength. The magnitude of this force depends on the sine of the angle between the current direction and the magnetic field, reaching its maximum when perpendicular.

Electromagnetism in Conductors

This concept involves understanding that an electromagnet generates a uniform or near-uniform magnetic field in a specific region, which then interacts with current-carrying conductors placed in that region. The interaction results in a Lorentz force, which is the net magnetic force on moving charges within the conductor.

Cross Product and the Right-Hand Rule

The calculation of the magnetic force involves the cross product of the vectors representing the conductor's length and the magnetic field. Using the right-hand rule helps determine the direction of the force, which is perpendicular to both the current direction and the magnetic field direction. This is crucial in predicting how the conductor will move within the magnetic field.

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