Concept explainers
(a)
The expression for energy stored in the capacitor
(a)
Answer to Problem 83PQ
The expression for energy stored in the capacitor
Explanation of Solution
Write the expression to find the equivalent capacitance of the capacitors connected in parallel.
Here,
Write the expression charge on
Here,
Write the expression to find the voltage across the parallel combination.
Here,
Substitute equation (I), (II) in (III) to find the voltage across the parallel combination.
Write the equation for initial energy in the capacitor
Here,
Write the equation for final energy in the capacitor
Here,
Substitute
Conclusion:
Re-write the expression using equation (IV).
Therefore, the expression for energy stored in the capacitor
(b)
Show that
(b)
Answer to Problem 83PQ
Explanation of Solution
Write the expression for
Re-arrange the above expression to find the maximum point for
Substitute
The denominator has to be minimum to maximize the
Differentiate
Differentiate the above expression to find the points of maxima and minima
The second derivative gives a positive value when
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Chapter 27 Solutions
Physics for Scientists and Engineers: Foundations and Connections
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- At a certain distance from a charged particle, the magnitude of the electric field is 500 V/m and the electric potential is 3.00 kV. (a) What is the distance to the particle? (b) What is the magnitude of the charge?arrow_forwardThe separation between the 4.40-cm2 plates of an air-filled parallel-plate capacitor is 0.230 cm. a. What is the capacitance of this capacitor? If the capacitor is connected to a 9.00-V battery, find b. the charge stored by the capacitor and c. the magnitude of the electric field between its plates.arrow_forwardA parallel-plate capacitor with an air gap has capacitance C0. It is connected to a battery with potential V0 that gives it charge Q0 and stored energy U0. After the capacitor is disconnected from the battery, a dielectric with constant = 3 is inserted into the air gap, completely filling it. In terms of the initial values, find the new capacitance C, charge Q, potential V, and stored energy U.arrow_forward
- A very large sheet of insulating material has had an excess of electrons placed on it to a surface charge density of 3.00nC/m2 . (a) As the distance from the sheet increases, does the potential increase or decrease? Can you explain why without any calculations? Does the location of your reference point matter? (b) What is the shape of the equipotential surfaces? (c) What is the spacing between surfaces that differ by 1.00 V?arrow_forward(a) Find the potential at a distance of 1.00 cm from a proton. (b) What is the potential difference between two points that are 1.00 cm and 2.00 cm from a proton? (c) Repeat parts (a) and (b) for an electron.arrow_forwardFigure P26.68 shows three small spheres with identical charges of 3.00 nC placed at the vertices of an equilateral triangle with side d = 2.50 cm. a. Is the electric potential due to the three spheres zero anywhere in the plane that contains the triangle, other than at infinity? b. What is the electric potential at the location of each sphere due to the other two spheres? FIGURE P26.68arrow_forward
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