Electric field of a point charge in uniform motion

In summary, In Griffiths Chapter 12, page 527, the discussion revolves around a point charge moving along the x-axis and the resulting electric fields. The questions raised include whether the vector R is solely in the x-y plane, what happened to the coordinate 'z', and why the calculations are only being done in a 2-D plane. The use of rotational symmetry is also considered. However, when the particle is assumed to be moving along the z-axis, the coordinates x, y, and z are defined as x=Rsinθcosø, y=Rsinθsinø, and z=Rcosø respectively. This results in a beautiful 3-dimensional representation that aligns with the usual definition of polar coordinates.
  • #1
unscientific
1,734
13
In Griffiths Chapter 12, pg 527:

Suppose a point charge is moving along x, we obtain the following E-fields:

Questions

1. Is the vector R solely in the x-y plane?

2. What happened to the coordinate 'z' ?

3. Why are they only doing things in the 2-D plane? Can we use rotational symmetry somewhere?

2ih5bn4.png
 
Last edited:
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  • #2
When instead, I assume the particle to be moving along z-axis it fixes everything!

and i use x=Rsinθcosø, y = Rsinθsinø, z = R cos ø

The end result turns out beautifully to be the one as described, in 3 dimensions:

2n9icmg.png



I suspect that since Polar coordinates is usually defined with θ as angle between R and z-axis and ø as angle in x-y plane, everything matches.
 
  • #3
bumpp
 

Related to Electric field of a point charge in uniform motion

What is an electric field?

An electric field is a physical quantity that describes the influence of an electric charge on other charges in its surroundings. It is represented by a vector and can be thought of as the force per unit charge at a given point in space.

What is a point charge?

A point charge is an idealized model of a charge that has no physical size or shape, and is considered to be located at a single point in space. It is typically represented by the letter 'q' and can be either positive or negative.

How is the electric field of a point charge calculated?

The electric field of a point charge is calculated using the equation E = k(q/r^2), where E is the electric field, k is the Coulomb's constant, q is the charge of the point charge, and r is the distance from the point charge to the point where the electric field is being measured.

What is uniform motion?

Uniform motion refers to the movement of an object at a constant speed in a straight line. In the context of electric fields, it means that the point charge is moving at a constant speed and in a straight line, without any acceleration.

How does the electric field of a point charge change with uniform motion?

The electric field of a point charge in uniform motion remains constant at all points in space, as long as the distance from the point charge is not changing. This is because the electric field is dependent on the charge and distance, and in uniform motion, the charge and distance do not change.

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