A beam of protons traveling at 1.20 km/s enters a uniform...

A beam of protons traveling at 1.20 km/s enters a uniform magnetic field, traveling perpendicular to the field. The beam exits the magnetic field, leaving the field in a direction perpendicular to its original direction ($\textbf{Fig. E27.24}$). The beam travels a distance of 1.18 cm $while$ $in$ $the$ $field$. What is the magnitude of the magnetic field?

Key Concepts

Circular Motion of Charged Particles

When a charged particle moves perpendicular to a magnetic field, the magnetic force acts as a centripetal force, causing the particle to move in a circular path. This circular motion is governed by the balance between the magnetic force (F = qvB) and the required centripetal force (F = mv²/r), allowing the determination of the radius of the particle’s path.

Lorentz Force

The Lorentz force describes the force that a charged particle experiences when it moves through a magnetic field. Specifically, when the velocity of the charged particle is perpendicular to the magnetic field, the force is given by F = qvB, which causes the particle to undergo a change in its direction of motion without affecting its speed.

Uniform Magnetic Field

A uniform magnetic field is characterized by a constant magnitude and direction throughout a specified region. This property ensures that any charged particle entering the field will experience the same magnetic force at every point within the region, leading to predictable motion patterns.

Radius of Curvature in a Magnetic Field

The radius of curvature for a charged particle moving in a magnetic field is found using the equation r = mv/(qB), where m is the mass, v is the speed, q is the charge, and B is the magnetic field strength. This relationship is crucial for analyzing how the particle’s path curves under the influence of the magnetic force, especially when the deviation from its initial direction is known.

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