- #1
Hypercube
- 62
- 36
Hello PF community,
I am currently self-studying electrodynamics from Griffiths textbook, and I'm at a point where the book discusses electrostatic boundary conditions. If someone can please check if my reasoning is right.
So, as I am approaching an infinite, uniformly charged plane (let the charge be positive), there is electric field pointing away from the plane, which has a magnitude equal to:
$$\vec E=\frac{\sigma}{2\epsilon_0}\hat n$$
where ##\hat n## is a vector perpendicular to the plane. This can be derived from Gauss' law, and it shows that electric field of a point does not depend on the distance from the plane. Magnitude on the other side of the plane would be the same, except it would have opposite direction.
However, according to the book, as I'm approaching the boundary and eventually cross it, there is a discontinuity. The author writes:
$$E_{above}-E_{below}=\frac{\sigma}{\epsilon_0}$$
Note that the author does not have these in bold. This implies that (somehow) the magnitude of the electric field above the plane is not equal to the magnitude of the electric field below it. How is that possible? I expected RHS to be 0 in this case.
Thanks.
I am currently self-studying electrodynamics from Griffiths textbook, and I'm at a point where the book discusses electrostatic boundary conditions. If someone can please check if my reasoning is right.
So, as I am approaching an infinite, uniformly charged plane (let the charge be positive), there is electric field pointing away from the plane, which has a magnitude equal to:
$$\vec E=\frac{\sigma}{2\epsilon_0}\hat n$$
where ##\hat n## is a vector perpendicular to the plane. This can be derived from Gauss' law, and it shows that electric field of a point does not depend on the distance from the plane. Magnitude on the other side of the plane would be the same, except it would have opposite direction.
However, according to the book, as I'm approaching the boundary and eventually cross it, there is a discontinuity. The author writes:
$$E_{above}-E_{below}=\frac{\sigma}{\epsilon_0}$$
Note that the author does not have these in bold. This implies that (somehow) the magnitude of the electric field above the plane is not equal to the magnitude of the electric field below it. How is that possible? I expected RHS to be 0 in this case.
Thanks.