Question

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

Explain your reasoning. Answer: No, a charged particle cannot move with constant speed in an electric field, as it will experience acceleration due to the net force acting on it. However, it is possible for a charged particle to move with constant speed in a magnetic field because the magnetic force only affects the direction of the particle's motion, not its speed.

Step-by-step solution

Analyzing the motion of a charged particle in an electric field

To understand the motion of a charged particle in an electric field, we can use the equation that quantifies the electric force acting on the charged particle: F_e = qE, where F_e is the electric force, q is the charge of the particle, and E is the magnitude of the electric field. As long as the particle has a non-zero charge, it will always experience a force (and therefore acceleration) in an electric field.

Determining the possibility of constant speed in an electric field

As we know from Newton's second law, a non-zero net force acting on an object will cause acceleration: F = ma. In the case of the charged particle in an electric field, it will experience a force (F_e) and hence acceleration. This means that the charged particle will not have a constant speed in an electric field as its velocity changes due to the acceleration.

Analyzing the motion of a charged particle in a magnetic field

Next, let's analyze the motion of a charged particle in a magnetic field. We can use the equation that quantifies the magnetic force acting on a charged particle: F_m = qvBsin(θ), where F_m is the magnetic force, q is the charge of the particle, v is the particle's velocity, B is the magnitude of the magnetic field, and θ is the angle between the velocity vector and the magnetic field vector.

Determining the possibility of constant speed in a magnetic field

In the case of a magnetic field, the magnetic force (F_m) is always perpendicular to the velocity vector (since sin(90°) = 1). This means that the magnetic force does not change the magnitude (speed) of the velocity but only its direction, leading to a circular or helical motion of the charged particle. The particle moves with constant speed in a magnetic field, but its direction is continually changing due to the magnetic force. Thus, it is possible for the charged particle to move with constant speed in a magnetic field. In conclusion, it is not possible for a charged particle to move with constant speed in an electric field due to the continuous net force and resulting acceleration. However, it is possible for the charged particle to move with constant speed in a magnetic field, as the force acting on the particle only changes its direction without affecting its speed.