What is the motion of a test charge in a non-uniform electric field?

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SUMMARY

The motion of a test charge in a non-uniform electric field is characterized by variable acceleration due to the changing electric forces acting on it. Unlike a uniform electric field where acceleration remains constant, a non-uniform field causes the test charge to accelerate at varying rates, which can include increasing or decreasing acceleration depending on the field's geometry and the charge's initial conditions. The direction of the electric field is opposite to the motion of a positive test charge, and the specific trajectory can vary significantly based on the initial velocity and position of the charge.

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  • Familiarity with Newton's second law of motion
  • Basic knowledge of charge behavior in electric fields
  • Concept of varying acceleration in physics
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Mr.somebody
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Homework Statement


Describe the motion of a test charge in a non-uniform electric field.By considering the electric forces acting and Newton’s second law, explain the type of motion occurring in a non-uniform electric field.

Homework Equations

The Attempt at a Solution


I wrote that the direction of the field is the opposite to the direction a test charge would move in.

the second question i don't understand at all ... I think it would be circular motion? Fc?
 
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Mr.somebody said:
I wrote that the direction of the field is the opposite to the direction a test charge would move in.
It does not have to be. You can shoot electrons into a field with a velocity perpendicular to the field, for example.

The motion will depend on the field, so it is hard to describe the motion in general. You can make a statement about the acceleration of the test charge, however.
 
in a uniform e-field the acceleration would be constant but in a non-uniform field it would accelerate at an increasing rate? Is this correct?
 
Mr.somebody said:
in a uniform e-field the acceleration would be constant but in a non-uniform field it would accelerate at an increasing rate? Is this correct?
Maybe at a decreasing rate ... maybe at a varying rate, up & down, changing direction, etc.
 
Mr.somebody said:
in a non-uniform field it would accelerate at an increasing rate? Is this correct?
We don't know unless we get the geometry of the field and the initial position and velocity of the electron.
 

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