Shortened

HM Schey: Div, grad, curl, and all that.
3e. 1997.


p.32, Using Gauss' Law to Find the Field:

Having rejected the two expressions for E [Equations (1-4) and (1-7)], we find that the only candidate left for providing us with a good general method for calculating the field is Gauss' law.

At first glance it does not appear to be a very likely candidate because, unlike Equations (1-4) and (1-7), it is not an explicit expression for E. That is, it does not say' 'E equals something." Rather, it says "The flux of E (the surface integral ofthe normal component of E) equals something."

Thus, to use Gauss' law, we must "disentangle" E from its surroundings. Despite this, there are situations in which Gauss' law can be used to find the field as an example will now show.

Having rejected the two expressions for E [Equations (1-4) and (1-7)], we find that the only candidate left for is Gauss' law.

At first glance it does not appear to be very likely because it does not say "E equals something." Rather, it says "The flux of E equals something."

Thus, to use Gauss' law, we must "disentangle" E from its surroundings, as an example will now show.

* * *

Shortened version by AI (POE: Assistant):

Gauss' law is the only candidate left for a good general method to calculate the electric field, despite not being an explicit expression for E.

While Gauss' law does not directly state "E equals something," it relates the flux of E to something else. To use Gauss' law, we must "disentangle" E from its surroundings.

Despite this challenge, there are situations where Gauss' law can be used to find the electric field, as the following example will demonstrate.

In Hemingway style:

Now, Gauss' law is the only way left to find the electric field in general. At first, it doesn't look promising because it doesn't just say "E equals this." It talks about the flux of E, not E itself. To use it, you have to pull E out of everything around it.

This is tough, but there are times when Gauss' law can get you the electric field. An example is coming up.