I'm having a little difficulty understanding the use of derivatives in Maxwell's equations. Eg. \oint E . dl = - \frac{d\varphi_{B}}{dt} this says that a changing magnetic flux in time, produces a potential difference (and electric field) in space? I noticed that its a full derivative, and its...
Hi, I was reading something on conservative fields, in this example \phi is a scalar potential. (Please refer to the attatched thumbnail). It's partial derivatives, but I'm not sure why the d\phi/dx * dx, the dx should cancel out? and that should leave d\phi. So the integral should be -3∫d\phi...
hmmm I understand what you say, do you mind explain this point a little further? sorry I know this is kind of a maths related question now. Thanks for the other posts and replies, I'm glad I got that cleared up =)
Hey guys!
So I've been trying to get my head around Divergence of a vector field. I do get the general idea, however I thought of a hypothetical situation I can't get my head around. Look at the second vector field on this page, http://mathinsight.org/divergence_idea
it has a negative...
Ok sorry I'm a little confused. F= \nabla \psi , where \psi is the scalar potential field, or potential energy? I have seen both in different places, or are they the same thing? From my understanding. A scalar potential field is a field which gives you a scalar value at a certain point. Am I...
I've been wrestling with this for a few days (not literally). I got confused because I read in a book that E = - ∇ \phi where E is the electric field and \phi is the scalar potential. However in my notes I had that for a conservative force F = -∇\phi. I got confused because electric force and...
If motion of an object obeys the wave equation, then it will display wave like behaviour. If you solve the wave equation, you get things like y = Asin \frac{2∏}{\lambda}(x - vt) which is a sinosodial wave. But from the second order differential equation v^{2}\frac{d^{2}y}{dx^{2}} =...
Homework Statement
I can't follow the math of the very last line.
It's really annoying me because I know its not supposed to be hard, I have tried multiplying top and bottom by k1+k2 and all kinds of rearranging but I'm not sure how they get from w1 - w2 / k1 - k2 = c (k1-k2) / (k1-k2)...
I see, I understand now, however what if if the sphere slides down the slope? would mechanical energy be conserved? I thought for it to slide there must be no friction present, so it would be conserved as none would be dissipated, if it rolls without slipping then since it is static friction...
Homework Statement
Find the area in the polar curve r = sin2θ between 0 and \frac{\pi}{2}.
The way to do this is to say the area of a tiny bit of this polar curve, dA = \frac{1}{2}r^{2}dθ
so the integral is just \frac{1}{2}\int^{\frac{\pi}{2}}_{0}(sin2θ)^{2}dθ
if we did say a function...
hmmm ok thanks for your help. To get the expression,
I got E1 = \frac{E0^{2} - m2^{2}c^{4}}{2E0}
Writing in full and pulling out some C from top and bottom
=\frac{c^{2}(p^{2} + m0^{2}c^{2} - m2^{2}c^{2}}{2c \sqrt{p^{2}+m0^{2}c^{2}}}
Now I'm a bit stuck because I got some p and some...
Hmmm ok I'm not sure if this is what you mean but this is what I did.
E2 = E0 - E1, I guess you want to square so you can use E^{2} = c^{2}p^{2} + m^{2}c^{4}
So if I square this I get E2^{2} = E0^{2} + E1^{2} - 2E1E0
Writing out E2^{2} in full and subbing E1 = cp I get
C^{2}P^{2} +...
Homework Statement
a Pion traveling at 0.93c decays into a muon which travels in the same direction and a neutrino which travels in the opposite direction. Use conservation of energy and momentum to find the energy of the muon as determined in the rest frame of the original pion. You should...
no no wait it gives the right answer if I do KE_{before} = KE_{AFTER} + KE _{explosion}
but how did you think of this? why can I ignore potential energy?
also the mass of each piece is 10kg as it breaks into equal fragments.