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 voltagesource by a thin wire. A switch in the circuit is closed at time t = 0 and a current I(t) flows in the circuit. Thecharge on the plate is related to the current according to I (t) = dq/dt. We begin bycalculating the electric field between the plates. Throughout this problem you mayignore edge effects. We assume that the electric field is zero for r > a.(A) Use Gauss’ Law to find the electric field between the plates as a functionof time t, in terms of q(t), a, ε, and π. The vertical direction is the k direction. (B)Now take an imaginary flat disc of radius r < a inside the capacitor, as shownbelow. Using your expression for E above, calculate the electric flux through this flatdisc of radius r < a in the plane midway between the plates, in terms of r, q(t), a,and ε. (C)Calculate the Maxwell displacement current, through the flat disc of radius r < ain the plane midway between the plates, in terms of r, I(t), and a.(D) Choose for an Amperian loop, a circle of radius r < a in the plane midwaybetween the plates. Calculate the line integral of the magnetic field around thecircle. (E)Would the direction of the magnetic field change if the plates were discharging?Justify your answer?
Sinusoids And Phasors
Sinusoids are defined as the mathematical waveforms that are used to describe the nature of periodic oscillations.
Circuit Theory
Electric circuits are a network that comprises of a closed-loop, which helps in providing a return path for the current through a switch. When the switch is activated, the load operates, and the current accepts a path to finish the circuit at a low potential level from the opposing high potential level. Electric circuits theory is a linear analysis that helps in establishing a linear relation of voltage and current for R (resistance), L (inductance), and C (capacitance).
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.
(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 direction.
(B)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.
(C)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.
(D) 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.
(E)Would the direction of the magnetic field change if the plates were discharging?
Justify your answer?
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