A 3.00 toroidal mH solenoid has an average radius of 5.60 cm and a cross-sectional area of 2.40 cm^2.

How many coils does it have? In calculating the flux, assume that B is uniform across a cross section, neglect the variation of B with distance from the toroidal axis.

At what rate must the current through it change so that a potential difference of 2.60 V is developed across its ends?

Question

A 3.00 toroidal mH solenoid has an average radius of 5.60 cm and a cross-sectional area of 2.40 cm^2.

How many coils does it have? In calculating the flux, assume that B is uniform across a cross section, neglect the variation of B  with distance from the toroidal axis.

At what rate must the current through it change so that a potential difference of 2.60 V is developed across its ends?

anonymous · Answer

WOW you got me on this one

anonymous · Answer

$$\epsilon = L \frac{di}{dt}$$$$\epsilon=N\frac{d\Phi_B}{dt}=N\pi r^2 B$$
You're given the emf, L, and r.  You can already find di/dt.  All you need to find N is to use Ampere's Law to find B, with C being the circle with the toroid's average radius.
$$\int_C \vec B.d\vec l=\mu_0 i_{enc}$$Hint: Visualize the torus and what part of it is going through the circle in order to get ienc.

anonymous · Answer

i have 8 mins and i dont think i can do that in time lol

anonymous · Answer

I did basically all of it!

anonymous · Answer

First equation: solve for di/dt.  Second equation: Find B using Ampere's Law with C being the path along the center of the circle cross sections of the torus, then solve for N.

anonymous · Answer

i tried pluging in and solving and i got the wrong answer
5mins!