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Chapter 18: Problem 8

Does the magnetic force ever do work on a moving charged particle?

Short Answer

Expert verified
No, the magnetic force does no work on a moving charged particle.

Step by step solution

01

Understand the Magnetic Force Equation

The magnetic force on a moving charged particle can be described by the equation \( F = q(v \times B) \), where \( q \) is the charge of the particle, \( v \) is the velocity vector of the particle, and \( B \) is the magnetic field vector. The force is perpendicular to both the velocity and the magnetic field.
02

Define 'Work' in Physics

Work done by a force is defined as \( W = F \cdot d \), where \( F \) is the force applied, and \( d \) is the displacement of the particle along the same direction as the force. Work is only done if the force has a component in the direction of the displacement.
03

Determine the Direction of Magnetic Force

From the equation \( F = q(v \times B) \), the force is perpendicular to the direction of the velocity \( v \). This means that the force never has a component in the direction of the particle's motion.
04

Apply the Conditions for Work

Since work requires that the force has a component in the direction of the displacement, and we determined that the magnetic force is always perpendicular to displacement, the magnetic force does no work on the charged particle.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Work in Physics
Work in physics is a measure of energy transfer. It can be thought of as the amount of effort required to move an object over a distance. The formula for work is given by \( W = F \cdot d \), where \( F \) represents the force applied to the object and \( d \) represents the displacement in the direction of the force.

For work to be done, a component of the force must act in the same direction as the displacement.
  • If an object's movement is perpendicular to the force, no work is done.
  • The SI unit of work is the joule (J).
  • If the force or displacement is zero, work is zero.
Understanding when and how work occurs helps us to analyze various phenomena in physics, like how a inclined plane makes moving an object easier.
Magnetic Field
A magnetic field is a region around a magnet where magnetic forces are exerted. It is represented by the symbol \( B \) and is measured in teslas (T).

Magnetic fields are essential in understanding electromagnetism, and they are visualized using field lines that show the direction and strength of the field.
  • The direction of a magnetic field is defined as the direction a north pole of a magnetic needle points.
  • The closer the field lines, the stronger the magnetic field.
Magnetic fields are crucial in explaining the behavior of charged particles. They interact with moving charges and are fundamental in the functioning of devices like electric motors and generators.
Charged Particle Dynamics
The dynamics of a charged particle moving through a magnetic field describes how the particle behaves under the influence of magnetic forces. When a charged particle enters a magnetic field, it experiences a magnetic force given by the equation \( F = q(v \times B) \), where \( q \) is the particle's charge, \( v \) is its velocity, and \( B \) is the magnetic field.

Key features of charged particle dynamics include:
  • The magnetic force acts perpendicular to both the velocity and the magnetic field.
  • This perpendicular force causes the particle to move in a circular or helical path, maintaining a constant speed and kinetic energy.
  • Because the force is perpendicular, it does not perform any work on the particle, as seen in situations where no energy is transferred to increase or decrease the speed.
Understanding these dynamics is vital for technologies that control charged particles, such as cyclotrons or particle accelerators.

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Most popular questions from this chapter

Two \(8.0-\mathrm{cm}\) -diameter circular wire loops lie directly atop one another. Find the magnetic field at the center of the common circle if each loop carries a current of \(7.5 \mathrm{~A}(\mathrm{a})\) in the same direction and (b) in the opposite direction.

A \(-50-\mu\) C charge moves vertically upward at \(75 \mathrm{~m} / \mathrm{s}\). Which magnetic field will produce a northward magnetic force of \(15 \mathrm{mN} ?\) (a) \(2 \mathrm{~T}\), east; (b) \(2 \mathrm{~T}\), west; (c) \(4 \mathrm{~T}\), east; (d) \(4 \mathrm{~T}\), west.

A square wire loop \(20 \mathrm{~cm}\) on a side lies in the \(x\) - \(y\) plane, its sides parallel to the \(x\) - and \(y\) -axes. The loop has 15 turns and carries a current of \(300 \mathrm{~mA}\), clockwise around the loop. Find the net force on the loop when there is a uniform magnetic field of strength \(0.50 \mathrm{~T}\) (a) in the \(+z\) -direction; (b) in the \(+x\) -direction; (c) along a diagonal of the square, from lower left to upper right.

A \(-200-\mu\) C charge moves vertically downward at \(12.3 \mathrm{~m} / \mathrm{s}\). Find the magnetic field (magnitude and direction) required to produce a northward magnetic force of \(1.40 \mathrm{mN}\).

The positron is a particle with the same mass as an electron but charge \(+e\). A positron in a bubble chamber moves perpendicular to a 4.0 -T magnetic field. If the positron's kinetic energy is \(25 \mathrm{eV},\) what's the radius of its trajectory in the bubble chamber? Sketch the tra jectory, assuming the magnetic field is directed vertically upward.
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