Chapter 29. The Electric Potential At any time, millions of light bulbs are transforming electric energy into light and thermal energy. Just as electric fields allowed us to understand electric forces, Electric Potential allows us to understand electric energy. Chapter Goal: To calculate and use the electric potential and electric potential energy. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

What are the units of potential difference? A.  Amperes B.  Potentiometers C.  Farads D.  Volts E.  Henrys

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What are the units of potential difference? A.  Amperes B.  Potentiometers C.  Farads D.  Volts E.  Henrys

The work W to move charge q through a potential difference V is: W= qV

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New units of the electric field were introduced in this chapter. They are:

A.  V/C. B.  N/C. C.  V/m. D.  J/m2. E.  Ω/m.

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New units of the electric field were introduced in this chapter. They are:

A.  V/C. B.  N/C. C.  V/m. D.  J/m2. E.  Ω/m.

The (differential) work to move charge q through a potential difference dV is dW= q dV = - q E dx E=- dV/dx

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The electric potential inside a capacitor A.  is constant. B.  increases linearly from the negative to the positive plate. C.  decreases linearly from the negative to the positive plate. D.  decreases inversely with distance from the negative plate. E.  decreases inversely with the square of the distance from the negative plate. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

The electric potential inside a capacitor A.  is constant. B.  increases linearly from the negative to the positive plate. C.  decreases linearly from the negative to the positive plate. D.  decreases inversely with distance from the negative plate. E.  decreases inversely with the square of the distance from the negative plate. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

Differential work to move charge q through a potential difference dV is dW= q dV = -q E dx -dV/dx = E If E is constant, V V=V0-Ex

We define the electric potential V (or, for brevity, just the potential) as

Charge q is used as a probe to determine the electric potential, but the value of V is independent of q. The electric potential, like the electric field, is a property of the source charges. The unit of electric potential is the joule per coulomb, which is called the volt V:

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The electric potential inside a parallel-plate capacitor is

where s is the distance from the negative electrode. The electric potential, like the electric field, exists at all points inside the capacitor. The electric potential is created by the source charges on the capacitor plates and exists whether or not charge q is inside the capacitor. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

QUESTIONS:

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Note: Dropping a proton through the 500 Volt potential difference will give it a high speed! Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

Consider two point charges, q1 and q2, separated by a distance r. The electric potential energy is

This is explicitly the energy of the system, not the energy of just q1 or q2. Note that the potential energy of two charged particles approaches zero as r approaches infinity . Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

Let q be the source charge, and let a second charge q', a distance r away, probe the electric potential of q. The potential energy of the two point charges is

By definition, the electric potential of charge q is

The potential extends through all of space, showing the influence of charge q, but it weakens with distance as 1/r. This expression for V assumes that we have chosen V = 0 to be at r = infinity. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

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QUESTIONS:

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Consider two point charges, +e and -e, separated by a distance r = 1.0e-10 m. The electric potential energy is

Define unit eV = electronvolt = 1.602 e-19 J, the energy a charge +e acquires in falling through a potential difference of 1 volt. The scale of potential differences in atoms is volts and the energy scale is eV. THAT is why atoms radiate/ absorb visible light quanta of similar energy. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

The electric potential V at a point in space is the sum of the potentials due to each charge:

where ri is the distance from charge qi to the point in space where the potential is being calculated. In other words, the electric potential, like the electric field, obeys the principle of superposition. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

2H

H2

To remove an electron from a neutral hydrogen takes 13.6 eV. Combining two hydrogen atoms permits both electrons to be between and close to two protons => binding energy of order eV released per atom pair. Binding of unlike atoms is asymmetric but the energy scale is the same: eV/bond. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

Two grams of H combine with 1/16 gm of O to form water. If 2H+O=>H2O released E=1 eV of “chemical energy,” what is the total energy release in joules and how high would that lift one kg subject to earth gravity?

Note: Demonstration ignited balloon filled with a mixture of H2 and O2. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

Two grams of H combine with 1/16 gm of O to form water. If 2H+O=>H2O released E=1 eV of “chemical energy,” what is the total energy release in joules and how high would that lift one kg subject to earth gravity? The number of molecules formed = the number of protons in one gm = the inverse of the proton mass (1.67e-24 gm) = Avogadro’s number N=6e23. The energy released is Q=N*E=6e23*1 eV That could raise 1 kg by Q=mgh=>h=Q/mg = 1000 m. Sweet! Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

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How much kinetic energy in eV is required to throw a proton at a Pb (Z=82) nucleus so the proton comes to rest just at the surface (r= 6 fm)?

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How much kinetic energy in eV is required to throw a proton at a Pb (Z=82) nucleus so the proton comes to rest just at the surface (R= 6 fm)? The nucleus has charge +Ze. To go from r=infinity to r=R, converting KE entirely to PE at r=R requires

To achieve this KE, the proton must be dropped through a potential difference of 20 MV=>Van de Graff accelerator. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.