A charged particle, passing through a certain region of space, has a velocity whose magnitude and direction remain constant.
(a) If it is known that the external magnetic field is zero everywhere in this region, can you conclude that the external electric field is also zero?
Explain.
(b) If it is known that the external electric field is zero everywhere, can you conclude that the external magnetic field is also zero?
Explain.
I will be happy to critique your thinking. It is not nice to post a lot of questions with each a different name. Usually, slackers or answer moochers do that.
I am sorry but you are mistaken. This is the first time I have been on this website in about 3 weeks. I have posted the question just above this one as well and another one just a minute ago for you to check my working. I will make an educated guess and repost the question.
(a) No, we cannot conclude that the external electric field is zero if the external magnetic field is zero everywhere in the region.
The motion of a charged particle in the absence of an external magnetic field is governed by the electric field. If the particle is experiencing a constant velocity, it implies that the net force acting on it is zero. In the absence of an external magnetic field, the only force acting on the charged particle is the electric force. Thus, for the particle to have a constant velocity, the external electric field must be zero.
However, the absence of a magnetic field does not necessarily imply the absence of an electric field. There could still be charges present within the region that produce an electric field. These charges may not be influencing the motion of the charged particle, but their electric field can still exist.
(b) Yes, if it is known that the external electric field is zero everywhere, we can conclude that the external magnetic field is also zero.
The motion of a charged particle in the absence of an external electric field is governed by the magnetic field. If the particle is experiencing a constant velocity, it implies that the net force acting on it is zero. In the absence of an external electric field, the only force acting on the charged particle is the magnetic force. Thus, for the particle to have a constant velocity, the external magnetic field must be zero.
This conclusion is based on the fact that a constant velocity can only be maintained when there are no net forces acting on the charged particle. If the external electric field is zero, and the particle is experiencing a constant velocity, it means that the external magnetic field is also zero.
(a) If it is known that the external magnetic field is zero everywhere in the region, we cannot necessarily conclude that the external electric field is also zero. The reason for this is that a charged particle with a constant velocity can still experience an electric field.
To understand this, we need to consider the forces acting on a charged particle. A charged particle moving with a constant velocity experiences a magnetic force and an electric force. The magnetic force is given by the equation F = qvB, where q is the charge of the particle, v is its velocity, and B is the magnetic field.
Since we know that the external magnetic field is zero, the magnetic force on the charged particle will be zero. However, the electric force is given by the equation F = qE, where E is the electric field. Even if the external magnetic field is zero, the charged particle can still experience an electric field and hence an electric force.
Therefore, we cannot conclude that the external electric field is zero based solely on the information that the external magnetic field is zero.
(b) If it is known that the external electric field is zero everywhere, we can indeed conclude that the external magnetic field is also zero, assuming no time-varying magnetic fields are present.
To understand this, we need to consider the forces acting on a charged particle. A charged particle moving with a constant velocity experiences a magnetic force and an electric force. The magnetic force is given by F = qvB, where q is the charge of the particle, v is its velocity, and B is the magnetic field. The electric force is given by F = qE, where E is the electric field.
If the external electric field is zero, and the charged particle has a constant velocity, there will be no electric force acting on the particle. Therefore, the only way for the net force to be zero is if the magnetic force is also zero. This implies that the external magnetic field is zero.
In conclusion, if it is known that the external electric field is zero everywhere, we can conclude that the external magnetic field is also zero, assuming no time-varying magnetic fields are present.