Motion of a Charged Particle in Electric & Magnetic Fields

In summary, the conversation discusses finding the equations representing the motion of a charged particle at rest in a uniform magnetic field and subjected to an oscillating electric field. The Lorentz force law is used to find the force and then substituted into Newton's Second Law. The direction of the electric and magnetic fields are not specified, so further calculations cannot be done. The solution also takes into account damping and resisting forces, leading to an oscillatory motion in the xz plane with a damping factor that eventually brings the particle to rest. The need for a full explanation of the problem is also mentioned.
  • #1
BishwasG
2
0
I can't figure out what is the motion of a charged particle at rest at origin in a constant uniform magnetic field when it is subjected to an oscillating electric field starting t = 0. I need to find the equations representing its motion.
 
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  • #2


Use the Lorentz force law[itex]\mathbf{F}=q(\mathbf{E}+\mathbf{v} \times \mathbf{B}) [/itex] where F is the force, q is the charge, E is the electric field and B is the magnetic field. Then, you substitute the resulting expression into Newton's Second Law, [itex]\mathbf{F}=m\mathbf{a}[/itex]. Then you just plug and chug and solve the resulting Diff. Eq. (You didn't specify the directions of the E and B fields, so I can't go any further. xP)

Hope that helps!
 
  • #3


E and B fields are perpendicular. I have to take into account the damping and resisting forces for the oscillatory motion. I need to find a solution analytically for the motion of the particle in that case. I managed to do it, but I am not sure if I did it right. If the B field is along y-axis and E along x, I found an oscillatory motion in xz plane. The damping factor brings it to rest as time goes to infinity.
 
  • #4


You should post the full details of the problem.
 
  • #5


The motion of a charged particle in electric and magnetic fields is a fundamental concept in physics. In this scenario, we have a charged particle at rest at the origin, which means it has an initial velocity of zero. This particle is then subjected to an oscillating electric field starting at t=0 and a constant uniform magnetic field. The question is asking for the equations that represent the motion of this particle.

To solve this problem, we can use the Lorentz force equation, which describes the force experienced by a charged particle in electric and magnetic fields. The equation is given by:

F = q(E + v x B)

Where:
F = force on the particle
q = charge of the particle
E = electric field
v = velocity of the particle
B = magnetic field

In this scenario, the electric field is oscillating, which means it changes with time. We can represent the electric field as:

E(t) = E0sin(ωt)

Where:
E0 = amplitude of the electric field
ω = angular frequency

Substituting this into the Lorentz force equation, we get:

F = q(E0sin(ωt) + v x B)

Since the particle is initially at rest, its velocity is zero. This means the term v x B also becomes zero. Therefore, the force experienced by the particle is given by:

F = qE0sin(ωt)

Now, to find the equations representing the motion of the particle, we need to use Newton's second law, which states that the net force on an object is equal to its mass multiplied by its acceleration. In this case, the acceleration of the particle is given by:

a = F/m

Where:
a = acceleration
m = mass of the particle

Substituting the force equation into this, we get:

a = (qE0sin(ωt))/m

This is a differential equation that describes the acceleration of the particle as a function of time. To find the equations representing the motion, we need to integrate this equation twice. The first integration will give us the velocity of the particle, and the second integration will give us the position of the particle.

After integrating twice, we get:

v = (qE0/mω)cos(ωt) + C1

x = (qE0/mω^2)sin(ωt) + C1t + C2

Where:
C1 and C
 

1. What is the equation for the motion of a charged particle in electric and magnetic fields?

The equation for the motion of a charged particle in electric and magnetic fields is known as the Lorentz force equation. It is given by F = q(E + v x B), where F is the force on the particle, q is the charge of the particle, E is the electric field, v is the velocity of the particle, and B is the magnetic field.

2. How does the direction of the magnetic field affect the motion of a charged particle?

The direction of the magnetic field affects the motion of a charged particle by exerting a force perpendicular to both the magnetic field and the particle's velocity. This force causes the particle to move in a circular or helical path, depending on the strength and direction of the magnetic field.

3. What is the difference between a uniform and non-uniform magnetic field?

A uniform magnetic field has the same strength and direction at every point in space, while a non-uniform magnetic field varies in strength and/or direction at different points. In the context of a charged particle's motion, a uniform magnetic field will result in a constant circular motion, while a non-uniform magnetic field will cause the particle's path to change over time.

4. How does the velocity of a charged particle affect its motion in electric and magnetic fields?

The velocity of a charged particle affects its motion in electric and magnetic fields by determining the strength of the forces acting on the particle. A higher velocity will result in a greater force, leading to a larger radius of curvature in the particle's path. In addition, the direction of the velocity plays a crucial role in determining the direction of the particle's motion in relation to the electric and magnetic fields.

5. Can a charged particle experience both electric and magnetic forces simultaneously?

Yes, a charged particle can experience both electric and magnetic forces simultaneously. This is due to the fact that the Lorentz force equation takes into account both the electric and magnetic fields when calculating the total force on the particle. The resulting motion of the particle will be a combination of both the electric and magnetic forces acting on it.

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