5.4.1 Example 12
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- čas přidán 28. 08. 2024
- 5.4.1 of Griffith's Introduction to Electrodynamics 2nd Ed
Find the A for an infinite solenoid.
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"he calls that cute...if you're into anime" lmao
how do we mathematically justify that the magnetic vector potential always points along the circumference of a given amperian loop with the same magnitude? I don't see how B being constant inside the solenoid implies this.
Thanks
Excellent explanation! Thank you
How to prove if del×A=B
thanks man
why u not upload 5.10 example......
How did you decide the direction of A?
+Aneree Mehta
A generally travels in the direction of the current, and the current of the solenoid travels through the wire, in the circular direction shown. The reasoning is written in the book as the paragraph after example 12.
The paragraph in question, copied out of the 4th edition of the Griffiths book.
"Typically, the direction of A mimics the direction of the current. For instance,
both were azimuthal in Exs. 5.11 and 5.12. Indeed, if all the current flows in
one direction, then Eq. 5.65 suggests that A must point that way too. Thus the
potential of a finite segment of straight wire (Pro b. 5.23) is in the direction of the
current. Of course, if the current extends to infinity you can't use Eq. 5.65 in the
first place (see Probs. 5.26 and 5.27). Moreover, you can always add an arbitrary
constant vector to A-this is analogous to changing the reference point for V, and
it won't affect the divergence or curl of A, which is all that matters (in Eq. 5.65
we have chosen the constant so that A goes to zero at infinity). In principle you
could even use a vector potential that is not divergenceless, in which case all bets
are off. Despite these caveats, the essential point remains: Ordinarily the direction
of A will match the direction of the current."