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Chapter 27: Problem 15

A charged particle moves under the influence of an electric field only. Is it possible for the particle to move with a constant speed? What if the electric field is replaced with a magnetic field?

Short Answer

Expert verified
Can it do so in a magnetic field? Explain your answer. Answer: A charged particle cannot move with a constant speed in an electric field, as the force it experiences due to the electric field causes it to either accelerate or decelerate. However, in a magnetic field, the force experienced by the charged particle is always perpendicular to its velocity vector, meaning that it does not change the particle's speed, only its direction. Therefore, it is possible for a charged particle to move with a constant speed in a magnetic field.

Step by step solution

01

Understanding the force on a charged particle in an electric field

A charged particle in an electric field experiences a force given by the formula: \(F_e = qE\), where \(q\) is the charge of the particle and \(E\) is the strength of the electric field. This force will cause the particle to accelerate or decelerate, which depends on the direction of the electric field and the charge of the particle.
02

Determining if a particle can move with a constant speed in an electric field

For a particle to move with a constant speed, the net force acting on the particle should be zero. In the case of an electric field, the charged particle experiences a force due to the field (\(F_e = qE\)). If there are no other forces acting on the particle, then it will always either accelerate or decelerate, making it impossible for the particle to move at a constant speed within an electric field.
03

Understanding the force on a charged particle in a magnetic field

A charged particle in a magnetic field experiences a force given by the formula: \(F_m = q(\mathbf{v} \times \mathbf{B})\), where \(q\) is the charge of the particle, \(\mathbf{v}\) is the velocity vector of the particle, and \(\mathbf{B}\) is the magnetic field vector. The force is always perpendicular to the velocity vector, which means that the magnetic force will not change the speed of the particle, only its direction.
04

Determining if a particle can move with a constant speed in a magnetic field

In the case of a magnetic field, the charged particle experiences a force that is always perpendicular to its velocity vector (\(F_m = q(\mathbf{v} \times \mathbf{B})\)). Since this force does not cause any change in speed, it is possible for the particle to move at a constant speed within a magnetic field.

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Most popular questions from this chapter

An electron with energy equal to \(4.00 \cdot 10^{2} \mathrm{eV}\) and an electron with energy equal to \(2.00 \cdot 10^{2} \mathrm{eV}\) are trapped in a uniform magnetic field and move in circular paths in a plane perpendicular to the magnetic field. What is the ratio of the radii of their orbits?

A current-carrying wire is positioned within a large, uniform magnetic field, \(\vec{B}\). However, the wire experiences no force. Explain how this might be possible.

Show that the magnetic dipole moment of an electron orbiting in a hydrogen atom is proportional to its angular momentum, \(L: \mu=-e L / 2 m,\) where \(-e\) is the charge of the electron and \(m\) is its mass.

A 30 -turn square coil with a mass of \(0.250 \mathrm{~kg}\) and a side length of \(0.200 \mathrm{~m}\) is hinged along a horizontal side and carries a 5.00 -A current. It is placed in a magnetic field pointing vertically downward and having a magnitude of \(0.00500 \mathrm{~T}\). Determine the angle that the plane of the coil makes with the vertical when the coil is in equilibrium. Use \(g=9.81 \mathrm{~m} / \mathrm{s}^{2}\).

An electron is traveling horizontally from the northwest toward the southeast in a region of space where the Earth's magnetic field is directed horizontally toward the north. What is the direction of the magnetic force on the electron?
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