(a) At what speed will a proton move in a circular path of...

Name: Problem 29, Chapter 11: University Physics
Uploaded: 2020-10-02T23:52:44-08:00
Duration: 3 min 14 s
Channel: Mayukh Banik
Description: (a) At what speed will a proton move in a circular path of the same radius as the electron in the previous exercise? (b) What would the radius of the path be if the proton had the same speed as the electron? (c) What would the radius be if the proton had the same kinetic energy as the electron? (d) The same momentum?

(a) At what speed will a proton move in a circular path of the same radius as the electron in the previous exercise? (b) What would the radius of the path be if the proton had the same speed as the electron? (c) What would the radius be if the proton had the same kinetic energy as the electron? (d) The same momentum?

Key Concepts

Lorentz Force

The Lorentz force is the fundamental force acting on a charged particle moving through a magnetic field. It is given by F = q(v × B) and is responsible for deflecting charged particles into circular or spiral paths. This concept underpins the analysis of charged particle dynamics in magnetic fields, which is essential when comparing the motion of different particles like protons and electrons.

Circular Motion in a Magnetic Field

In a uniform magnetic field, a charged particle experiences a force perpendicular to its velocity which causes it to move in a circular path. The radius of this path is determined by the equation r = mv/(qB), where m is the mass, v is the velocity, and q is the charge of the particle, highlighting how differences in mass and charge affect the trajectory.

Kinetic Energy

Kinetic energy, defined as KE = ½ mv², measures the energy a particle possesses due to its motion. When comparing particles with different masses, holding the kinetic energy constant results in different speeds, a key point when assessing how the path radius changes under conditions of equal kinetic energy.

Momentum

Momentum, expressed as p = mv, is a measure of the quantity of motion a particle carries. Analyzing situations where particles have the same momentum is crucial because even with identical momentum, differences in mass lead to different velocities, thereby affecting the radius of their circular paths in a magnetic field.

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