Calculating Charge and Current in a Region Between Concentric Conducting Spheres

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The discussion focuses on calculating the charge Q(t) on an inner conducting sphere and the current I(t) in the region between two concentric conducting spheres filled with a material of conductivity σ and dielectric constant k. The inner sphere is connected to a battery, and upon disconnection at t=0, the charge and current need to be analyzed over time. The electric field between the spheres is crucial for determining the charge. The decay constant for the charge is established as kεo/σ, which is essential for understanding the behavior of the system after the battery is disconnected. The conversation emphasizes the importance of the electric field in deriving these equations.
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Homework Statement


The region between concentric conducting spheres is filled with a material with conductivity σ and dielectric constant k. The inner sphere (radius a) is connected to the positive terminal of a battery with emf Vo, and the outer sphere (radius b) is connected to the negative terminal. At t=0 the batter is disconnected.
(a) Calculate Q(t), the charge on the inner conductor, and sketch a plot of this function. Show that the decay constant is kεo/σ.
(b) Calculate I(t).


The Attempt at a Solution


How do I go about this question?
 
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Hi PhysicsUnderg! :smile:

Hint: what is the electric field between the spheres when the charge is q ? :wink:
 

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