Understanding Cylindrical Vector Fields: Can They Be Electrostatic?

[taishar]

I'm given this:

A vector field is given in cylindrical coordinates as:

F=(A)(s)(PhiHat) + (B)(z)(zhat)

Where A and B are constants. Could F be an electrostatic field ? Why or why not ?

I kind of feel stupid asking this because I feel like I should know, but, I'm currently braindead after having just spent hours doing the previous 29 problems.

Thanks,
Dan

 

[Brad Barker]

I'm given this:

A vector field is given in cylindrical coordinates as:

F=(A)(s)(PhiHat) + (B)(z)(zhat)

Where A and B are constants. Could F be an electrostatic field ? Why or why not ?

I kind of feel stupid asking this because I feel like I should know, but, I'm currently braindead after having just spent hours doing the previous 29 problems.

Thanks,
Dan

an electrostatic field should be curl-less.

so... take the curl and see if it's zero or not.

 

[Brad Barker]

i guess i should provide some justification for my answer so that you'll believe me!

an electrostatic field can be written in terms of a scalar potential:

$$\mathbf{E} = -\nabla V.$$


and it is a mathematical fact that
$$\nabla \times \nabla V = 0$$

for any V.


So if the curl is strictly zero, this implies that E can be expressed in terms of a scalar potential (and not have a vector potential term), and this is enough to determine if E is a static field or not.

 

[taishar]

Duh. I knew I was just being stupid. I had to do a couple similar problems earlier. Gah. Thanks a bunch :) Too many hours doing homework...