Ah, right. So I would have to multiply what I got before by 4∏ for it to be accurate, which would give me:
120.192 = dB/dt
So I'll go out on a limb here and state that then I can find the emf (which is just d/dt(magnetic flux)) by multiplying this rate of change by the area encased by the...
Oh, so could I use the equation for B, but differentiate it so it's the equation for dB/dt, which becomes:
dB/dt = μ0/(4∏)*N*dI/dt /d
Which, if I plugged everything in, would give me:
dB/dt = 10 ^ -7 * 350 * 106577.23 /.39 = 9.5646 T/s
Oh, so dI/dt is:
dI/dt = emf(battery)/R(R/L * e^((-R/L)t)) = emf(battery)/L * e^((-R/L)t)
So dI/dt is
9/(6.07613*10^-5) * e^((-20/(6.07613*10^-5))*10^-6) = 106577.23 A/s
So now that I have dI/dt and I have L, how do I use that to find the current if it doesn't involve the emf?
Ah, so it's what I got for my emf, but also divided by the change in time, which is 10^-6 seconds?
So for my emf instead of 7.6688 * 10^-6 V, I'll have 7.6688 V?
I don't think that was my only problem, but if that was one of them, I'm glad to know.
Okay! So first I'll find the current going through the solenoid so I can find its inductance. I'll use the formula for an RL circuit current:
I = emf(battery)/R*(1-e^(-R/L)t)
L = μ0N^2/d*∏R^2
So I'll find L first because I'll need it for I:
L = 4∏*10^-7*(350)^2/.39*∏(.007)^2 =...
I really can't figure this out. I've tried using the area of the rectangle as my area for the flux instead of inside the solenoid, I've tried using the current equation given for an RL circuit, and other associated things. I even looked up some problems I thought were comparable and solved...
Hmm. I was using B*A, but there wouldn't be an A of the outside of a solenoid. I tried a slightly different tact where I found the current using the formula I listed above, and then used:
emf(inducted) = μ0*N^2/d*∏R^2*dI/dt
And then divided the result by the resistance of the rectangular...
Thanks! I tested that out, though, and it doesn't look like that's my only problem because I still got the answer wrong. Is there anything else I'm doing incorrectly?
Hi there! Thanks for the welcome! :)
So does that mean that I'd need to use the formula:
I = emf(battery)/R (1-e^(-R/L*t))
instead? Where R is the resistance of the resistor and L is the inductance proportionality constant?
Homework Statement
Connect a battery to a solenoid
A cylindrical solenoid 40 cm long with a radius of 8 mm has 250 tightly-wound turns of wire uniformly distributed along its length (see the figure). Around the middle of the solenoid is a two-turn rectangular loop 3 cm by 2 cm made of...