Electrical Energy and Capacitance

Electrical Energy and Capacitance

Chapter 18

Electrical Potential Energy

Electrical Potential Energy - potential energy associated with an object due to its position relative to a source of electric force.

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PEelectric=-qEd+ charge – charge

Toward ELoses PEelectric

Gains PEelectric

Opposite EGains PEelectric

Loses PEelectric


Electrical Potential Energy in a Uniform Electric Field


Electrical Potential Energy for a Pair of Charges

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PEelectric=kcq1q2

r

Potential DifferenceSection 18-2

Electric Potential – at any point in an E-field is the potential energy of a test charge at that location divided by the value of that test charge.

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ElectricPotential=PEelectric

charge

Potential Difference

Potential Difference – the change in electrical potential energy associated with a charged particle divided by the charge of the particle.

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ΔV =ΔPEelectric

q


Potential Difference in a Uniform Electric Field

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ΔPEelectric=−qEd

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ΔV =Δ(−qEd)

q

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ΔV =−EΔd


Potential Difference between an infinite distance and some location near a point charge

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ΔV =kcqr

ProblemsSection 18-2

Two large, charged parallel plates are 4.0 cm apart. The magnitude of the electric field between them is 625 N/C. a) What is the potential difference between the plates? b) What work is done moving a charge equal to that of one electron from one plate to another?


A voltmeter measures the potential difference between two large parallel plates to be 60.0 V. The plates are 3.0 cm apart. What is the magnitude of the electric field between them?


The electric field intensity between two large, charged, parallel metal plates is 8000 N/C. The plates are 0.05 m apart. What is the potential difference between them?


A voltmeter reads 500 V when placed across two charged, parallel plates. The plates are 0.020 m apart. What is the electric field between them?


What potential difference is applied to two metal plates 0.500 m apart if the electric field between them is 2500 N/C?


What work is done when 5.0 C is raised in potential by 1.5 V?


Using a zero reference potential at infinity, determine the amount by which a point charge of 4.0 x 10-8 C alters the electric potential at a spot 1.2 m away when the charge is (a) positive and (b) negative.


At locations A and B in the figure, find the total electric potential due to the two point charges.AB0.20 m0.20 m0.40 m +8.0×10

−9 C −8.0×10−9 C

CapacitanceSection 18-3

Capacitance – the ability of a conductor to store energy in the form of electrically separated charges.

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C =QΔV


Capacitance for a Parallel-Plate Capacitor

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C =ε0Ad

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ε0 =8.85 ×10−12 C2

Nm2


Electrical Potential Energy stored in a charged capacitor

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PEelectric=12

QΔV

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PEelectric=12

C(ΔV )2

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PEelectric=Q2

2C


1. (a) How much charge is on each plate of a 4.00 µF capacitor when it is connected to a 12.0 V battery?

(b) If the same capacitor is connected to a 1.50 V battery, what charge is stored?


2. A parallel-plate capacitor has an area A = 2.00 x 10-4 m2 and a plate separation d = 1.00 mm. Find the capacitance.


3. If the voltage on a capacitor doubles, the amount of charge that can be stored by that capacitor __________.

A. doubles

B. is halved

C. is quadrupled

D. is unchanged

E. None of these


4. How much charge is stored by a 1.5 µF capacitor when 1.0 V is maintained across its terminals?

A. 1.0 µC

B. 0.67 MC

C. 1.0 µF

D. 1.5 x 10-6 CE. none of these


5. How might you double the capacitance of a parallel plate capacitor?

A. double the area and the separation

B. double the area and halve the separation

C. double either the dielectric constant, or the area, or halve the separation

D. double either the dielectric constant, the area or the separation

E. none of these


6. How much energy is stored in a 3.0 µF capacitor when it is placed across the terminals of a 12 V battery?

A. 4.3 x 10-4 J

B. 1.8 x 10-5 J

C. 24 x 106 J

D. 2.2 x 10-4 J

E. none of these

Electrical Energy and Capacitance

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