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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

The magnetic field in a region in space (where \(x>0\) and \(y>0\) ) is given by \(B=(x-a z) \hat{y}+(x y-b) \hat{z},\) where \(a\) and \(b\) are positive constants. An electron moving with a constant velocity, \(\vec{v}=v_{0} \hat{x},\) enters this region. What are the coordinates of the points at which the net force acting on the electron is zero?

An electron is moving at \(v=6.00 \cdot 10^{7} \mathrm{~m} / \mathrm{s}\) perpendicular to the Earth's magnetic field. If the field strength is \(0.500 \cdot 10^{-4} \mathrm{~T}\), what is the radius of the electron's circular path?

A straight wire of length \(2.00 \mathrm{~m}\) carries a current of \(24.0 \mathrm{~A} .\) It is placed on a horizontal tabletop in a uniform horizontal magnetic field. The wire makes an angle of \(30.0^{\circ}\) with the magnetic field lines. If the magnitude of the force on the wire is \(0.500 \mathrm{~N}\), what is the magnitude of the magnetic field?

A charged particle is moving in a constant magnetic field. State whether each of the following statements concerning the magnetic force exerted on the particle is true or false? (Assume that the magnetic field is not parallel or antiparallel to the velocity.) a) It does no work on the particle. b) It may increase the speed of the particle. c) It may change the velocity of the particle. d) It can act only on the particle while the particle is in motion. e) It does not change the kinetic energy of the particle.

A particle with a charge of \(+10.0 \mu \mathrm{C}\) is moving at \(300 \cdot \mathrm{m} / \mathrm{s}\) in the positive \(z\) -direction. a) Find the minimum magnetic field required to keep it moving in a straight line at constant speed if there is a uniform electric field of magnitude \(100 . \mathrm{V} / \mathrm{m}\) pointing in the positive \(y\) -direction. b) Find the minimum magnetic field required to keep the particle moving in a straight line at constant speed if there is a uniform electric field of magnitude \(100 . \mathrm{V} / \mathrm{m}\) pointing in the positive \(z\) -direction.
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