In general, a function is Even if
F(x) = F(-x)
and a function is Odd if
F(x) = -F(-x)
So consider in your case
F(x) = -\frac{x^2}{x^3+x}
Look now at F(-x) :
F(-x) = -\frac{(-x)^2}{(-x)^3+(-x)}
= -\frac{x^2}{-x^3-x}
= \frac{x^2}{x^3+x}
= -F(x)
So your function is Odd...
(1) it's true that there's bound charge in the dielectric. Would you agree however that there's no free charge in the dielectric. If so, then we can use equation (4.22) of Griffiths (3rd ed.) and obtain:
\nabla \cdot \textbf{D}=0
because \rho_f=0
Since the material is a linear...
Hi, I'm new to the forum, and I hope I'm not posting this under the wrong thread. I'm studying for quals, and I've come across this past exam:
Homework Statement
http://www.physics.uiuc.edu/education/graduate/Qual/sm/SMSpring07B.pdf
This is a problem on the Landau theory of phase...
From the way the question is phrased, I would believe the B-field is oriented in the "up" direction; this is because in general the energy of a magnetic dipole in a magnetic field is:
-\mu \cdot B
so the dipole will want to align with the field to get to the lowest energy. In this case...