Concept explainers
(a)
The stored energy in the system as function of
(a)
Answer to Problem 65AP
The energy stored in the system is
Explanation of Solution
The following figure shows the metal block of length
Figure (1)
Any charge that appears on any of the plate of the capacitor will induce an equal magnitude and opposite sign of charge on the nearby surface of the slab. The slab has zero net charge and zero electric field inside it.
Write the expression for capacitance.
Here,
From figure (1), the area of the metal inside the capacitor is
The value of dielectric constant for the partially filled capacitor with metal is
Substitute
The value of capacitance for the portion where, metal is not inserted is,
Substitute
The value of the whole capacitance is,
Substitute
Write the expression for charge in the capacitor.
Here,
For the whole conductor, the value of
Substitute
The value of the charge for the portion where, metal is not inserted is,
Substitute
Write the expression for the energy stored in the capacitor.
Here,
Substitute
Conclusion:
Therefore, energy stored in the system is
(b)
The magnitude and direction of force that acts on the metallic block.
(b)
Answer to Problem 65AP
Magnitude of the force is
Explanation of Solution
Write the expression for force.
Here,
Substitute
Conclusion:
Therefore, the magnitude of the force is
(c)
The stress on the advancing front face of the block.
(c)
Answer to Problem 65AP
The stress on the advancing front face of the block is
Explanation of Solution
The advancing front face area is,
Write the expression for stress.
Here,
Substitute
Therefore, the stress on the advancing front face of the block is
(d)
The energy density in the electric field between the charged plates in terms of
(d)
Answer to Problem 65AP
The energy density in the electric field is
Explanation of Solution
Write the expression for energy density.
Here,
Substitute
Therefore, the energy density in the electric field between the charged plate is
(e)
The comparison of part (c) with part (d).
(e)
Answer to Problem 65AP
The stress is equal to the energy density in the electric field between the charged plates.
Explanation of Solution
Compare the energy density with the stress that is comparing the equation (VI) with equation (VIII).
Therefore, the stress is equal to the energy density in the electric field between the charged plates.
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Chapter 26 Solutions
Bundle: Physics for Scientists and Engineers with Modern Physics, Loose-leaf Version, 9th + WebAssign Printed Access Card, Multi-Term
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