A capacitor consists of two circular plates of radius a separated by a distance d (assume d << a). The centre of each plate is connected to the terminals of a voltage source by a thin wire. A switch in the circuit is closed at time t = 0 and a current I(t) flows in the circuit. The charge on the plate is related to the current according to I (t) = dq/dt. We begin by calculating the electric field between the plates. Throughout this problem you may ignore edge effects. We assume that the electric field is zero for r > a. Use Gauss’ Law to find the electric field between the plates as a function of time t, in terms of q(t), a, ε, and π. The vertical direction is the k Now take an imaginary flat disc of radius r < a inside the capacitor, as shown below. Using your expression for E above, calculate the electric flux through this flat disc of radius r < a in the plane midway between the plates, in terms of r, q(t), a, and ε. Calculate the Maxwell displacement current, through the flat disc of radius r < a in the plane midway between the plates, in terms of r, I(t), and a. Choose for an Amperian loop, a circle of radius r < a in the plane midway between the plates. Calculate the line integral of the magnetic field around the circle. Would the direction of the magnetic field change if the plates were discharging? Justify your answer?
. A capacitor consists of two circular plates of radius a separated by a distance d (assume d << a). The centre of each plate is connected to the terminals of a voltage source by a thin wire.
A switch in the circuit is closed at time t = 0 and a current I(t) flows in the circuit. The charge on the plate is related to the current according to I (t) = dq/dt. We begin by calculating the electric field between the plates. Throughout this problem you may ignore edge effects. We assume that the electric field is zero for r > a.
- Use Gauss’ Law to find the electric field between the plates as a function of time t, in terms of q(t), a, ε, and π. The vertical direction is the k
- Now take an imaginary flat disc of radius r < a inside the capacitor, as shown below.
Using your expression for E above, calculate the electric flux through this flat disc of radius r < a in the plane midway between the plates, in terms of r, q(t), a, and ε.
- Calculate the Maxwell displacement current, through the flat disc of radius r < a in the plane midway between the plates, in terms of r, I(t), and a.
- Choose for an Amperian loop, a circle of radius r < a in the plane midway between the plates. Calculate the line integral of the magnetic field around the circle.
Would the direction of the magnetic field change if the plates were discharging? Justify your answer?
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