A proton moves at 7.50 ×10^7 m / s perpendicular to a magnetic field. The field causes the proto

step 1 Hi everyone, so the problem asks what is the magnetic field in which proton is moving in a circu

A proton moves at 7.50 ×10^7 m / s perpendicular to a...

A proton moves at $7.50 \times 10^{7} \mathrm{m} / \mathrm{s}$ perpendicular to a magnetic field. The field causes the proton to travel in a circular path of radius 0.800 $\mathrm{m} .$ What is the field strength?

Key Concepts

Lorentz Force

The Lorentz force is the force exerted on a charged particle moving in a magnetic field. It acts perpendicular to both the velocity of the particle and the magnetic field, causing the particle to change direction without altering its speed, which is crucial when determining the path of the particle in the field.

Centripetal Force

Centripetal force is the net force required to keep an object moving in a circular path. In the context of a charged particle moving in a magnetic field, the Lorentz force provides the centripetal force necessary for circular motion, linking the magnetic field strength to the particle’s radius and speed.

Uniform Circular Motion

Uniform circular motion describes the motion of an object traveling at constant speed along a circular path. The balance between the inward centripetal force and the object’s inertia ensures that the path remains circular, which is a key concept when analyzing scenarios where magnetic fields cause such motion.

Relationship between Magnetic Field and Particle Motion

This concept involves understanding that the magnetic field strength can be deduced by equating the magnetic Lorentz force to the centripetal force required for circular motion. This relationship integrates the particle's charge, velocity, and the radius of its circular path, providing a method to calculate the magnetic field impacting the particle.

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