I think i was wrong. ##\frac{1}{2} \frac{B^2}{ \mu}## is energy density. I think I must multiply it by ##A * x## for the part that has the core and by ##A * (L-x)## for the part that hasn't. Beside this, Is my way correct.
For the subscript and superscript and actually any formula, you must...
I will get ##B## as ##B_{with~ core} = \mu n I ## and ##B_{without~core} = \mu_0 n I##, Right? And the energy of ##B## field is ##\frac{1}{2}\frac{B^2}{\mu}## where ##\mu## is the magnetic permittivity of that region of space. is this Right? Should I say that sum of these two energies of ##B##...
I don't know how to solve this with energy? How is that? I just know energy is ##\frac{1}{2} L i^2##. But I don't know how to use this the calculate inductance in this question.
For finding magnetic field ##B##, We see this question like two Solenoids. for the first one, we have ##\int B ds = \mu I## so ##B x_0 = \mu I n x_0 ## so ##B = \mu n I##. For the second one we have ##B = \mu_0 n I##. For the Inductance we have ##L = \mu l n^2 A## so we have ##L_1 = \mu x_0...
I know that ##B = \mu n I## and ##\phi = B \pi R^2##. So with have ##d\phi / dt = \mu n \alpha \pi R^2##. But I don't know what to do with this? is this the answer? I don't think so but I don't know what to do after this.
I) For the first part I used:
##V = - \int E ds = \int_a^c \frac{1}{4\pi\epsilon_0} Q /r^2 dr+ \int_c^{c+d} \frac{1}{k} \frac{1}{4\pi\epsilon_0} Q /r^2 dr + \int_{c+d}^b \frac{1}{4\pi\epsilon_0} Q /r^2 dr ##
And by using ##C = Q/V## We get an answer which is somehow large for writing here...
Maybe we can say that if this thing happens for ##m_{i-1} , m_{i} , m_{i+1}## and they do not fit the expected pattern, then if we consider a ##v## for ##m_{i-1}##, then the energy (velocity) transferred to ##m_{i+1}## will not be maximum. However, I think maybe there should be a way to solve...
Homework Statement
My problem has two parts.
1) We have two point masses ##m,M##. and there is another mass ##m_1## between them.They are all aligned in a line. Mass ##M## is moving with speed ##u_1## toward ##m_1## and after collision and all other masses are not moving. we want to find...
Finally, It means that if I solve this two equations in terms of ##V_R## and ##V_S## I will get the answers wanted by the problem, (##u = V_s## , ##v = V_r - V_s##. Is this right? The only think odd is that in the actual question I had with numerical values, there where values for...
I think mgr is because the COM will not contact the ground. ##h## is measured from the ground to the COM. and when the ball hits the ground, COM will be ##r## meters above the ground. About ##\omega##, I know it is actually ##\omega r = v## and the mistake was a typo. But can you explain why I...
At the end of slid, the vertical component will ##V_r## at that point. there will be no vertical component I think. And the speed relative to ground will be ##V_r - V_s##. So shoud I write ##(Initial Momentum)~~~~ 0 + 0 =(Final Momentum)~~~~ m (V_r - V_s) + M (-V_s)## and ##mgh = mgr + 1/2~ m...
Do you mean Normal component relative to the slide? (perpendicular to slide). I can't completely understand how to write this terms because I don't actually know any angle here. the only thing I can write is that the v of COM of ball relative to a stationary observer is ##\vec{V_s} + \vec{V_r}##
At first, I wanted to solve it like the usual inclines. But at this one, it seems we don't have a fixed angle and I can't write something like ##cos \theta##. Maybe the conservation of energy could help here but I don't know how to write it for the whole system. I am not sure whether I should...
The original question is not in English.
The first part is only some given numbers (eg. ##\mu_s = 0.7##) which is actually not important in general solution and I didn't write them because I don't want numerical solution. After these numbers, It is said that we release a ball from height h from...
Homework Statement
We have a ball of mass ##m##and radius ##r##. it is placed on an incline (We don't know the angle of the incline, nor we do whether the angle is constant along the incline - maybe it is a curved incline) and then released. The COM of ball is ##h## meters above the incline at...