Is the Magnitude of an Electric Field Consistent Across All Spatial Locations?

[BadSkittles]

Hello, in an electric field, are the magnitudes of the field the same regardless of the spatial location? Or is the field's magnitude similar to the force experienced by the test charge where it gets smaller as you move away from the source charge? Any clarification would be appreciated.

 

[Simon Bridge]

Hello, in an electric field, are the magnitudes of the field the same regardless of the spatial location? Or is the field's magnitude similar to the force experienced by the test charge where it gets smaller as you move away from the source charge? Any clarification would be appreciated.

By definition: The magnitude of the field is the same as the magnitude of the force experienced by a test charge with a charge q, divided by q. (The direction is the same as the force experienced by a positive test charge.)

i.e. we write: $\vec{E} = \vec{F}/q$

In general, the magnitude of the field varies from place to place.
You should be able to tell this - if the field were the same no matter where you were then how would it be useful?

 

[rude man]

The test charge must be arbitrarily small so as not to affect the E field being measured. So really E = lim q → 0 of F/q.

 

[Simon Bridge]

Technically, the test charge has to be small enough not to disturb the charge configuration giving rise to the field being measured.

There's a more detailed discussion:
https://www.physicsforums.com/showthread.php?t=611066