Chapter 24 Electric Potential In this chapter we will define the electric potential ( symbol V ) associated with the electric force and accomplish the following tasks: Calculate V if we know the corresponding electric field. Calculate the electric field if we know the corresponding potential V. Determine the potential V generated by a point charge. Determine the potential V generated by a discrete charge distribution. Determine the potential V generated by a continuous charge distribution. Determine the electric potential energy U of a system of charges. Define the notion of an equipotential surface. Explore the geometric relationship between equipotential surfaces and electric field lines. Explore the potential of a charged isolated conductor. (24-1)

O x . xi xf F(x) A B (24-2)

Checkpoint 1: In the figure, a proton moves from point i to point f in a uniform electric field directed as shown. Does the electric field do positive or negative work on the proton? Does the electric potential energy of the proton increase or decrease? c) Does the force do positive or negative work? d) Does the proton move to a point of higher or lower potential?

A B (24-3)

Electric potential is a scalar property associated with an electric field, regardless of whether a charged object has been placed in that field; it is measured in joules per coulomb or volts. V Electric potential energy is an energy of a charged object in an external electric filed ( or more precisely, an energy of the system consisting of the object and the external electric field); it is measured in joules. U

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S A B  V q S V (24-11)

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Checkpoint 3: The figure here shows a family or parallel equi potential surfaces ( in cross section) and five paths along which we shall move an electron from one surface to another. What is the direction of the electric field associated with the surfaces? For each path, is the work we do positive, negative, or zero? Rank the paths according to the work we do, Greatest first.

O (24-4)

r1 r2 r3 P q1 q3 q2 (24-5)

Checkpoint 4: The figure here shows three arrangements of two protons, Rank the arrangements according to the net electric potential produced at point P by the protons, Greatest First

A B V V+dV (24-13)

A B V V+dV (24-14)

x y O q1 q2 q3 r12 r23 r13 (24-15)

y O x y  q1 Step 1 x O r12 q1 q2  Step 2 Step 3 x y O r12 r13 r23 q1 (24-16)

path A B conductor (24-17)

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R (24-20)

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