Recent content by besebenomo

I tried to solve it considering the canonical ensemble (since the system is at the equilibrium with temperature T) and started finding the partition function:The problem is I am not sure if I have done it correctly and need help because I don't really know where to check.

Force might be smaller?

Thank you again for the reply Force is ##\vec{F} = i \vec{l} \times \vec{B}##, the only thing that changed in here is the current which is the derivative wrt time of the (total?) flux divided by R. I just can't make my mind whether in region 2, ##\Phi(B)_{region1}## and ##\Phi(B)_{region2}##...

Flux, and then the derivative of the flux doesn't exist at that point, so no e.m.f. But, before doing any computations, I wanted to understand it more conceptually. The bar in the first region should decelerate... Then there is no force in 0, and if it didn't stop before reaching that point...

Sorry if I post again about this topic (last time I promise!) but I still have some doubts regarding the concept of flux. This collection of problems I have quite standard but there are so many variations. Here is the circuit in question: Something tells me that I could write a function that...

Thanks a lot you've been really helpful!

The force acting on the bar is the magnetic force, in this case: $$\vec{F}_{mag} = i \vec{l}\times \vec{B} = - \frac{-B_{0} v(t) (2l-x(t)) l}{R} (B_{0} - B_{0} \frac{x(t)}{2l})$$ Then I solve the differential equation, if I didn't make mistakes along the way: $$m \frac{dv(t)}{dt} = -...

Yes sorry, I meant B is depending on the x-coordinate. Yes, I know. The problem is that I am not used to solving differential equation when also ##x(t)## is the equation... Is there any way I can rewrite ##i## as a function of only ##v(t)##? That way would be so much easier to solve. Maybe I...

The amplitude of ##\vec{B}## is given by: $$B(x) = B_{0} - B_{0} \frac{x}{2l}$$ for ##0 \leq 0 \leq 2l## This was my attempts at finding the flux of B: $$\Phi(B) = (B_{0} - B_{0} \frac{x}{2l})(2l-x(t))l = B_{0}2l^2-2B_{0}x(t)l+ B_{0}\frac{x(t)^2}{2}$$ and the current: $$ i = -\frac{d...

E thank you

$$B(t) = B_{0} \frac{t^2}{T^2}$$ for ##0 \leq t \leq T## The issue here is more conceptual, because once I find the flux of B I know how to proceed to find the current. I got velocity (but it seems to me that it is the initial velocity), I could use it to find the time in function of space...