# Sketching equipotentials for a moving charge

• CAF123
In summary, the conversation discusses the equipotentials of a point charge that is initially stationary at the origin before being displaced at a uniform speed to a new position R. At t = R/c, the charge is at position R/2 and the equipotentials are centered around this point. For t = 4R/c, the charge is at position 2R and the equipotentials are centered around this point until a maximum radius of 4R, beyond which they are centered at the origin.
CAF123
Gold Member

## Homework Statement

A point charge remains stationary at the origin for a long time but then, at time t = 0, is displaced, at uniform speed c/2, to a new position R, where it stops.

Sketch with care the equipotentials of ##\phi## at a time t = R/c, and then again at time t = 4R/c. Your sketches should including distances both large and small compared to R.

## Homework Equations

[/B]
retarded time ##t_R = t - |r-r'|/c##

## The Attempt at a Solution

[/B]
What is t? the position of the charge or the retarded position as measured by some observer? Assuming the former, when ##t=R/c,## the charge is at position R/2. So ct=R and so we have circles centered around the point R/2. Outside R, the equipotentials are those from when the charge was at origin. So should draw circles centered at R/2 and with radii between 0 and R?

Similar analysis for t=4R/c, the charge is at 2R and ct=4R so have circles centered at 2R until max radius 4R. Beyond that, have circles centered at origin. Is it right?

Such a fast motion will introduce magnetic fields, and make the concept of a potential alone problematic, but I guess we have to ignore this problem here.

tR determines your fields, t is the current time. That will give different circles.
CAF123 said:
Outside R, the equipotentials are those from when the charge was at origin.
Right.
CAF123 said:
Similar analysis for t=4R/c, the charge is at 2R and ct=4R so have circles centered at 2R until max radius 4R. Beyond that, have circles centered at origin. Is it right?
The transition region is more complicated.

## 1. What are equipotential lines?

Equipotential lines are imaginary lines drawn on a diagram to indicate points that have the same potential (or voltage). These lines are always perpendicular to electric field lines and represent a constant potential value.

## 2. How do you sketch equipotential lines for a moving charge?

To sketch equipotential lines for a moving charge, you need to first determine the direction of the electric field at different points around the charge. Then, draw lines perpendicular to these electric field lines to represent points with the same potential. The spacing between these lines should decrease as you move closer to the charge.

## 3. What is the significance of equipotential lines for a moving charge?

Equipotential lines for a moving charge help to visualize the electric field and potential around the charge. They also show how the potential changes as you move closer or further away from the charge.

## 4. How do the equipotential lines change as the charge moves?

As the moving charge changes position, the equipotential lines will also change. They will become closer together as the charge moves closer to the point and further apart as the charge moves away. The direction of the lines will also change to reflect the changing electric field direction.

## 5. Can you sketch equipotential lines for a moving charge in three dimensions?

Yes, equipotential lines for a moving charge can be sketched in three dimensions. In this case, the lines will form concentric spheres around the charge, with the spacing between the lines decreasing as you move closer to the charge. The lines will also change direction as the charge moves in three dimensions.

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