Concept explainers
(a)
The proof that the displacement current in the capacitor gap has the same value as the
(a)
Answer to Problem 38P
The displacement current in the capacitor gap has the same value as the conduction current in the capacitor leads/
Explanation of Solution
Given:
The radius of the circular plateis
The separation distance between the plates is
Formula used:
The expression for displacement current is given by,
The expression for electric flux is given by,
The expression for electric field strength between the plates of the capacitor is given by,
Calculation:
The displacement current is evaluated as,
Solve further as,
Here,
Conclusion:
Therefore, the displacement current in the capacitor gap has the same value as the conduction current in the capacitor leads.
(b)
The direction of pointing vector in the region between the capacitor plates.
(b)
Explanation of Solution
Introduction:
The Poynting vector is a quantity which describes the magnitude and direction of the flow of energy in
The electric field
Using the equation of pointing vector the direction of
Conclusion:
Therefore, the direction of pointing vector is radially inward.
(c)
The expression for poynting vector in the region between the capacitor plates and to prove that flux into the region between the plates is equal to the rate of change of the energy stored in the capacitor.
(c)
Answer to Problem 38P
The expression for poynting vector in the region between the capacitor plates is
Explanation of Solution
Formula used:
The expression for Ampere’s Law is given by,
The expression for total energy stored in the capacitor is given by,
Calculation:
The direction of
The diagrammatical representation is shown below.
Figure 1
Applying Ampere’s law to a closed circular path of radius
In vector notation
Substituting
Here,
The total energy in the capacitor is calculated as.
The rate at which energy is stored in the capacitor is calculated as,
Further solve as,
The energy flowing into the solenoid per unit time is written as,
Further solve as,
So, the flux into the region between the plates is equal to the rate of change of the energy stored in the capacitor
Conclusion:
Therefore, the expression for poynting vector in the region between the capacitor plates is
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Chapter 30 Solutions
Physics for Scientists and Engineers
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