Motion of an electron in a nonuniform magnetic field

In summary, the conversation discusses the trajectory of an electron shot towards an infinitely long wire with high current flowing through it. The possibility of circular motion is ruled out due to the changing force, leading to the suggestion of an ellipse as the possible curve. It is suggested to use Newton's Second Law and Lorentz Force in the right coordinate system to determine the equation for the electron's motion.
  • #1
ChessEnthusiast
115
3

Homework Statement


An electron is shot towards an infinitely long wire with high current flowing througuh it.
Please, look at my "sketch" in the attachment.
How will its trajectory be affected? What curve will it be?

2. The attempt at a solution
I thought about circular motion, but the fact that force changes rather rules that out.
What about an ellipse?
 

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  • #2
ChessEnthusiast said:

Homework Statement


An electron is shot towards an infinitely long wire with high current flowing througuh it.
Please, look at my "sketch" in the attachment.
How will its trajectory be affected? What curve will it be?

2. The attempt at a solution
I thought about circular motion, but the fact that force changes rather rules that out.
What about an ellipse?

Did you write the expression for the force on the electron?
 
  • #3
ChessEnthusiast said:
thought about circular motion, but the fact that force changes rather rules that out.
What about an ellipse?
I believe it can't be just guessed. You need to write an equation, most likely a differential equation.
 
  • #4
cnh1995 said:
I believe it can't be just guessed. You need to write an equation, most likely a differential equation.

I would suggest combining Newton's Second Law with Lorentz Force, using the right coordinate system, and then work from there.
 

FAQ: Motion of an electron in a nonuniform magnetic field

What is a nonuniform magnetic field?

A nonuniform magnetic field is a magnetic field that varies in strength and/or direction within a given area. This means that the force exerted by the field on a charged particle, such as an electron, will also vary within that area.

How does a nonuniform magnetic field affect the motion of an electron?

A nonuniform magnetic field will cause an electron to experience a force that is not constant in magnitude or direction. This means that the electron's path will be curved and it will accelerate or decelerate as it moves through the field.

Can an electron be in equilibrium in a nonuniform magnetic field?

Yes, it is possible for an electron to be in equilibrium in a nonuniform magnetic field. This occurs when the force from the magnetic field is balanced by another force, such as an electric force, acting on the electron.

How is the motion of an electron in a nonuniform magnetic field calculated?

The motion of an electron in a nonuniform magnetic field can be calculated using the Lorentz force equation, which takes into account the strength of the magnetic field, the velocity of the electron, and its charge. Other factors, such as the mass of the electron and any additional forces, may also need to be considered in more complex scenarios.

What practical applications rely on an understanding of the motion of an electron in a nonuniform magnetic field?

An understanding of the motion of an electron in a nonuniform magnetic field is crucial in many areas of science and technology. Some examples include particle accelerators, magnetic resonance imaging (MRI) technology, and the design of electronic devices such as computer hard drives and speakers.

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