8:06 AM
@JohnRennie Sir I’m learning Green’s Theorem. My book writes $$\mathbf A = U \nabla V - V \nabla U$$ and , consequently, for $A_n$ $$A_n = U \frac{\partial V}{\partial n} - V \frac{\partial U}{\partial n}$$
I don’t know how they got that formula for $A_n$

I've no idea what the argument is there. Which book is this?
To be honest I long ago forgot the proof for most of the theorems I use so I'm not the best person to ask.

2 hours later…
10:01 AM
@JohnRennie Sommerfeld's Lecture on Theoretical Physics

@Knight Which volume?

Volume 2, Section Theorems of Gauss, Stokes and Green
A_n is just the component of $\maghbf A$ along any surface $\sigma$
Closed surface*

10:16 AM
Page 24?

@JohnRennie yes
@JohnRennie yes

I'm not sure I see the point of equation (11)

@JohnRennie Yes sir
@JohnRennie That’s just the assumption.

I guess he is just saying define some scalar functions $U$ and $V$ such that we can write $\mathbf A$ in terms of these functions.

We’re imaging a field which can be written like that.
@JohnRennie Yeah

10:24 AM
I can't see how to get (12) from (11). Sorry.

I think $A_n$ is the component of $A$ along a normal unit vector i.e. $A_n = \mathbf A \cdot \mathbf {\hat{n}}$

😭
@JohnRennie Yes. Let’s take for simplicity $$\mathbf A = U ~grad V$$ $$\mathbf A \cdot n = U \frac {\partial V}{\partial x} n_x + \frac{\partial V}{\partial y} n_y + \frac{\partial V}{\partial z}n_z$$

I guess that must mean $$\frac{\partial V}{\partial n} = \frac {\partial V}{\partial x} n_x + \frac{\partial V}{\partial y} n_y + \frac{\partial V}{\partial z}n_z$$

Really?
Thank you so much sir :-)

8 hours later…
6:25 PM
23?
Can anyone help with this please.