What is the energy of a toroidal solenoid with given dimensions and current?

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The discussion revolves around calculating the energy of a toroidal solenoid with specific dimensions and current. The user initially calculated the cross-sectional areas and attempted to find the energy using different formulas, but encountered discrepancies in the results. They calculated an energy of 4.08J and a current of 6.44A, but faced confusion with their formulas. After some back-and-forth, they acknowledged a potential arithmetic error in their calculations and ultimately resolved the issue. The conversation highlights the importance of verifying formulas and calculations in physics problems.
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Homework Statement


[/B]
N=600 (number of loops)
a1=200mm
a2=240mm
h=40mm
δ=1,5mm or l0
S0=1,1*S (Cross sectional area)
B0=1,2T

I need to find energy of toroid and currect going through it.
Solution: W=4,08J, I=6,44A
Capture.PNG

2. The attempt at a solution

So far I managed to calculate S and S0:
S=(a2-a1)*h
S=0,0016m2
S0=1,1*S
S0=0,00176m2I tried to find energy using this formula but it's not correct:
W0=B02*S0*l0/2*μ0
W0=1,51J

W=B*H*S*(l-l0)/2 (B and H are from the graph)
W=4,76J

Formula for current is I=NH/l but since nothing is correct I didn't bother to try and calculate it.
 
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I see nothing wrong with your formula for W0 and W unless you made an arithmetic error which I suspect you did. For example, I got W = 2.34J.
Your formula I=NH/l is wrong however so not using it was ironically a good move! :smile:
 
Last edited:
Never mind. I figured it out. Thanks !
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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