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Magazine Chapter 4: Q43E (page 987)
Displacement Current in a Dielectric. Suppose that the parallel plates in Fig. 29.23 have an area of 3.00 cm2 and are separated by a 2.50-mm-thick sheet of dielectric that completely fills the volume between the plates. The dielectric has dielectric constant 4.70. (You can ignore fringing effects.) At a certain instant, the potential difference between the plates is 120 V and the conduction current iC equals 6.00 mA. At this instant, what are (a) the charge q on each plate; (b) the rate of change of charge on the plates; (c) the displacement current in the dielectric?
Short Answer
Answer:
(a) When the dielectric constant 4.70and at a certain instant the potential difference between the plates is 120 V and the conducting current is equals tothen the charge on q on each plate is
(b) The rate of change of the charges on the plates is
(c) The displacement current in the dielectric is
Step by step solution
Calculating the rate of change of charge on the plates
It is given the potential difference between the plates isV=120 V, and the conducting current is , and the circular plates have an area of , where the separation is by a thick sheet of dielectric, and the constant of K=4.70
Now, the charge over the plate is:
q=CV
the capacitance of a parallel plate capacitor is given by:
Therefore:
Therefore, the charge on is
Now, the rate of change of conduction current is:
Displacement current
To find the displacement current in the dielectric, the displacement current is:
Or,
The electric field between the plates of the capacitor isandTherefore:
Jd=jc
Therefore the displacement current is
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