Jump to content

proof that in general curl of B field is uJ


Tor Fredrik

Recommended Posts

image.thumb.png.5b036535b8bbbca7e41c8a1458ffd14c.png 

Above they derive that curl of B is uJ. I know they use the identity

image.png.0ef8145198fb6e8aa2be787267594499.png

So since as underlined above that the derivatives of J is 0 we have that

image.png.a7ea5b4b6dc5f82939ce5dd99e4efe67.png

But my problem is why is the derivative of J 0 in general. I have looked at a derivation for this:

  

image.thumb.png.33ca2221ad74764b945e801749fd5053.png

And the end of this derivation is the following

image.png.90a5f4f50e5d0e5e937442536ee431cc.png

But in the derivation they use that acceleration is constant and that it is a function of E showed in the orange box above. But E does not have to be constant since it is a function of r? So how is this a general derivation for the fact that divergence of current density is 0? 

Link to comment
Share on other sites

58 minutes ago, swansont said:

One of the conditions of the derivation is that the current in the wire is constant.  

 

Why would that lead to that the divergence of the current density is 0. Can you show it mathematically?

Edited by Tor Fredrik
Link to comment
Share on other sites

1 hour ago, Tor Fredrik said:

Why would that lead to that the divergence of the current density is 0. Can you show it mathematically?

The derivative of any constant is zero. That's such a basic understanding I'm not surprised it's not explicitly written down.

 

dC/dx = 0 for C = a constant

Link to comment
Share on other sites

Create an account or sign in to comment

You need to be a member in order to leave a comment

Create an account

Sign up for a new account in our community. It's easy!

Register a new account

Sign in

Already have an account? Sign in here.

Sign In Now
×
×
  • Create New...

Important Information

We have placed cookies on your device to help make this website better. You can adjust your cookie settings, otherwise we'll assume you're okay to continue.