You know the speed that the boys are moving (and thus the initial velocity of the bears) as well as their relative positions (which will give you the initial velocity vectors). You should be able to use the kinematic equations to solve for the trajectories of the bears once released and thus...
damn it, i knew it was something that simple. of course the result of the curl operation will be a vector quantity that is perpendicular to both k and H. Then the dot product of perpendicular vectors is zero. Thanks for kicking me in the head ;D
Hi, I was looking at an EM problem today and realized I wasn't sure why
(kxH)\dotk = 0
I tried writing it out explicitly and got (w 1,2,3 representing directions)
A1(A2*B3-A3*B2) - A2(A1*B3-A3*B1) + A3(A1*B2-A2*B1)
and I can't see why this should equal zero. This is troubling...
The idea is to compute the average force on the dipole from a dielectric sphere placed in a uniform electric field, also oriented in the d-direction. I think I got it figured out though. The idea is to define an angle theta with respect to the d-direction, and then integrate over the solid...
Oops, I did make one mistake. The last term in the equation should be \left( p \cdot \hat d \right) p Other than that everything should be correct.
e is the dielectric constant in gaussian units. p is the dipole moment. \hat d is a unit vector in the d-direction.
I just have a quick question about finding the average force of a dipole.
I am given the expression (after I derived it anyway):
\textbf{F} = -3 \left( \frac{e-1}{e+2} \right) \frac{R^{3}}{d^{7}} \left[4( p \bullet \hat d)^{2} \hat d + p^{2} \hat d - (p \bullet \hat d) \hat d \right]...
I have a quick question about vector spaces.
Consider the vector space of all polynomials of degree < 1. If the leading coefficient (the number that multiplies x^{N-1}) is 1, does the set still constitute a vector space?
I am thinking that it doesn't because the coefficient multiplying...
Ya, I got that down. So I was thinking that this integral should be equal to zero because we are evaluating r at 0. But I wasn't sure if that was right or if since we are integrating over a delta function, the whole thing should be equal to q. or 4 \pi q . Ya, I'm a little confused
I am trying to integrate a charge density over a volume in order to obtain a total charge, but there is a delta function involved and I am not entirely sure how to treat it.
\rho = q* \delta (\textbf{r})- \frac {q\mu^{2} Exp(- \mu r)} {4 \pi r}
Q = \int \rho (\textbf{r})d^{3}r...