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Advanced Physics Homework Help
How to find the charge at time = t (at any instant)
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[QUOTE="asadahmad_7869, post: 6248340, member: 668554"] [B]Homework Statement:[/B] A circuit consists of a coil with inductance ##L## and an uncharged capacitor of capacitance ##C##. The coil is in a constant uniform magnetic field such that the flux through the coil is ##\phi##. At time ##t = 0##, the magnetic field was abruptly switched off. Let ##\omega_0= \frac{1}{\sqrt(LC)}## and ignore the resistance of the circuit. Then, 1) Magnitude of charge on the capacitor is ##|Q(t)|= 2C \omega_0\phi\sin(\omega_o t)## 2) Magnitude of charge on the capacitor is ##|Q(t)|= C \omega_0\phi\sin(\omega_o t)## 3) Initial current in the circuit is infinite. 4) The cyclotron frequencies of all the particles are same. It is a more than one correct type, with the answers being 2 and 4. [B]Relevant Equations:[/B] Charge on Capacitor ## Q = CV ## Emf induced in inductor ##V (or E) = -\frac{d\phi}{dt}## I was not able to derive the charge on the capacitor. But then, I arbitrarily assumed ##\phi=B.A## (Dot product of Magnetic field and Area) Then, proceeding as follows, ##\phi=BA\cos(\omega_0 t)## ##\frac{d\phi}{dt}=−BA\omega_0\sin(\omega_0 t)## Now at ##t=0, \phi=BA\cos(0)=BA## Therefore, ##\frac{d\phi}{dt}=−\phi\omega_0\sin(\omega_0 t)## Now, ##V(t)=−\frac{d\phi}{dt}## ##V(t)=\phi\omega_0\sin(\omega_0 t)## And finally, ##Q(t)=CV(t)## ##Q(t)=C\phi\omega_0\sin(\omega_0 t)## Which corresponds to option 2. Now, since I arbitrarily assumed the value of ##\phi##, I don't know if it is correct. Please help me with any other alternative to this question? Also, I don't understand the 4th option. Can you help in that as well? Thank You. [/QUOTE]
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How to find the charge at time = t (at any instant)
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