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tourjete
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Homework Statement
Grad student here, reviewing for my quals. It's been awhile since E&M and I think I need a refresher since this problem has me stumped.
A planar circuit surrounds a solenoid and consists of two capacitors of capacitances [itex]C_1[/itex] and [itex]C_2[/itex] joined together by normal wires. The solenoid crosses the plane of the circuit in a patch of area A, and it produces a time-dependent magnetic field that is changing linearly with time: [itex]B(t) = B_0 + \frac{dB}{dt} t[/itex], the positive direction is coming up out of the paper. The field is uniform inside the solenoid and the magnetic field outside the solenoid is the be neglected.
Before the field is applied the capacitors have zero charge. In equilibrium what are the charges [itex]Q_1[/itex] and [itex]Q_2[/itex] on the capacitors? Determine the signs.
Homework Equations
Q = CV
Faraday's Law
Lenz's Law
The Attempt at a Solution
I found the flux: [tex] \Phi = AB(t) = A(B_0 + \dot{B} t)[/tex]. I then used Faraday's law to find the induced voltage: [tex] \Delta V = - N \frac{\Delta \Phi_B}{\Delta t} = - \frac{\Delta BA}{\Delta t} = -A \frac{dB}{dt}[/tex].
However, the capacitors are in series which means that they should have the same charge and different voltages, right? I feel like I'm combining two competing concepts here.
As for the signs, I think that they should be opposite but I'm not sure, that's just intuition.
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