What is the unique drift speed for a charged particle in crossed E and B fields?

In summary, the student is stuck and does not know how to solve a problem. They first write down the equation of motion and separate it into three components. They then prove that there is a unique value of v_{x0} for which the particle moves undeflected through the fields. They are then lost and do not know how to solve for v_{x} using the second equation. They miss an absolute value of v in their equations for a.
  • #1
num1cutiey
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Homework Statement



I am working on a problem and don't know if I am going about it right because I am stuck.

A charged particle of mass m and positive charge q moves in uniform electric and magnetic fields, E pointing in the y direction and B in the z direction (an arrangement called "crossed E and B fields"). Suppose the particle is initially at the origin and is given a kick at time t=0 along the x axis with v[tex]_{}x[/tex]=v[tex]_{x0}[/tex] (positive or negative). (those are supposed to be subscripts but I can't get it to work)

(a) Write down the equation of motion for the particle and resolve it into it's three components. (done) Show that the motion remains in the plane z=0 (done)

(b) Prove that there is a unique value of v[tex]_{x0}[/tex], called the drift speed v[tex]_{dr}[/tex],for which the particle moves undeflected through the fields. (This is what I can't get)

Homework Equations



F=ma
F=q(E+vXB)

The Attempt at a Solution



I wrote down the equation of motion and when separated I got

v[tex]_{y}[/tex]*B[tex]_{z}[/tex]=m*dv[tex]_{x}[/tex]/dt
v[tex]_{x}[/tex]*B[tex]_{z}[/tex]=m*dv[tex]_{y}[/tex]/dt
0=m*dv[tex]_{z}[/tex]/dt

I proved the whole z=o plane thing.

Now I get to b

Iknow that x(t)=f some arbitrary function and y(t)=0. (We already know z(t)=0). So I used the second equation above and solve it to get y(t)=(v[tex]_{x}[/tex]*B[tex]_{z}[/tex]*t^2)/2m=0. Ok so what do I do from here. I am lost I can divide everything and get v[tex]_{x}[/tex]=0 but I know that is wrong. Did I go about this the wrong way??
 
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  • #2
E is in the y direction. So is vxB, since v is along x and B is along z. You just have to pick an absolute value of v so the total of all the forces, E+vxB=0.
 
  • #3
shoot I missed the E in the y direction in my equations for a)! Thanks!
 

FAQ: What is the unique drift speed for a charged particle in crossed E and B fields?

What is the definition of drift speed of a particle?

The drift speed of a particle is the average velocity at which the particle moves in a specific direction due to an applied electric field. It is a measure of how fast the particle moves through a material.

How is the drift speed of a particle calculated?

The drift speed of a particle can be calculated by dividing the current (I) by the cross-sectional area (A) of the material and the number of charge carriers (n) present in the material, multiplied by the charge of the particle (e). This can be represented by the formula: v = I/(neA).

What factors affect the drift speed of a particle?

The drift speed of a particle is affected by the strength of the applied electric field, the number of charge carriers in the material, and the material's resistivity. Additionally, the temperature and impurities in the material can also impact the drift speed.

Why is drift speed important in materials science?

Understanding the drift speed of particles is crucial in materials science because it helps in analyzing the electrical properties and behavior of materials. It also plays a significant role in the design and development of electronic devices, such as semiconductors and circuits.

How does the drift speed of a particle relate to current flow?

The drift speed of a particle is directly proportional to the current flow in a material. This means that as the drift speed increases, the current flow also increases. This relationship is described by Ohm's law, which states that the current in a material is equal to the drift speed multiplied by the material's cross-sectional area and the number of charge carriers.

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