Chapter 24. Electric Potential. 24.1. What is Physics? 24.2. Electric Potential Energy 24.3. Electric Potential 24.4. Equipotential Surfaces 24.5. Calculating the Potential from the Field 24.6. Potential Due to a Point Charge
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24.1. What is Physics?
24.2. Electric Potential Energy
24.3. Electric Potential
24.4. Equipotential Surfaces
24.5. Calculating the Potential from the Field
24.6. Potential Due to a Point Charge
24.7. Potential Due to a Group of Point Charges
24.8. Potential Due to an Electric Dipole
24.9. Potential Due to a Continuous Charge Distribution
24.10. Calculating the Field from the Potential
24.11. Electric Potential Energy of a System of Point Charges
24.12. Potential of a Charged Isolated Conductor
Note: Electric energy is one type of energy.
The reference point can be anywhere. For convenience, we usually set charged particles to be infinitely separated from one another to be zero potential energy
The potential energy U of the system at any point f is
where W∞ is the work done by the electric field on a charged particle as that particle moves in from infinity to point f.
A proton, located at point A in an electric field, has an electric potential energy of UA = 3.20 × 10-19 J. The proton experiences an average electric force of 0.80 × 10-9 N, directed to the right. The proton then moves to point B, which is a distance of 1.00 × 10-10 m to the right of point A. What is the electric potential energy of the proton at point B ?
The electric potential V at a given point is the electric potential energy U of a small test charge q0 situated at that point divided by the charge itself:
If we set at infinity as our reference potential energy,
SI Unit of Electric Potential: joule/coulomb=volt (V)
The electric potential difference between any two points i and f in an electric field.
Three points, A, B, and C, are located along a horizontal line, as Figure 19.4 illustrates. A positive test charge is released from rest at A and accelerates toward B. Upon reaching B, the test charge continues to accelerate toward C. Assuming that only motion along the line is possible, what will a negative test charge do when it is released from rest at B?
The work done by the electric force as the test charge (q0=+2.0×10–6 C) moves from A to B is WAB=+5.0×10–5 J. (a) Find the difference, ΔU=UB–UA, in the electric potential energies of the charge between these points. (b) Determine the potential difference, ΔV=VB–VA, between the points.
Determine the number of particles, each carrying a charge of 1.60×10–19 C (the magnitude of the charge on an electron), that pass between the terminals of a 12-V car battery when a 60.0-W headlight burns for one hour.
Two identical point charges (+2.4×10–9 C) are fixed in place, separated by 0.50 m. (see Figure 19.32). Find the electric field and the electric potential at the midpoint of the line between the charges qA and qB.
An equipotential surface is a surface on which the electric potential is the same everywhere.
What will happen if the electric field E is not perpendicular to the equipotential surface?
The drawing shows a cross-sectional view of two spherical equipotential surfaces and two electric field lines that are perpendicular to these surfaces. When an electron moves from point A to point B (against the electric field), the electric force does +3.2×10–19 J of work. What are the electric potential differences (a) VB–VA, (b) VC–VB, and (c) VC–VA?
The potential gradient gives the component of the electric field along the displacement Δs
The sketch below shows cross sections of equipotential surfaces between two charged conductors that are shown in solid black. Various points on the equipotential surfaces near the conductors are labeled A, B, C, ..., I. At which of the labeled points will the electric field have the greatest magnitude
The metal contacts of an electric wall socket are about 1.0 cm apart and are maintained at a potential difference of 120 V. What is the average electric field strength between the contacts? What is the direction of the electric field if the left contact is the higher potential? The lower potential? Treat the potential difference between the contacts as being constant in time.
The electric potential at any point on the central axis of a uniformly charged disk is given by Eq. 24-37 ,
Starting with this expression, derive an expression for the electric field at any point on the axis of the disk.
An excess charge placed on an isolated conductor will distribute itself on the surface of that conductor so that all points of the conductor—whether on the surface or inside—come to the same potential. This is true even if the conductor has an internal cavity and even if that cavity contains a net charge.
(a) Figure 24-5a shows two points i and f in a uniform electric field E . The points lie on the same electric field line (not shown) and are separated by a distance d. Find the potential difference ΔV by moving a positive test charge q0 from i to f along the path shown, which is parallel to the field direction. (b) Now find the potential difference ΔV by moving the positive test charge q0 from i to f along the path icf shown in Fig. 24-5b.
A zero reference potential is at infinity
The potential at a point due to any number of point charges can be found by simply finding the potential at the point due to each alone and adding the potentials: Vtot=V1+V2+∙∙∙+VN
In Fig. 24-12a, a thin nonconducting rod of length L has a positive charge of uniform linear density λ . Let us determine the electric potential V due to the rod at point P, a perpendicular distance d from the left end of the rod.
In Section 22.7 , we calculated the magnitude of the electric field at points on the central axis of a plastic disk of radius R that has a uniform charge density σ on one surface. Here we derive an expression for V(z), the electric potential at any point on the central axis.
The electric potential energy of a system of fixed point charges is equal to the work that must be done by an external agent to assemble the system, bringing each charge in from an infinite distance.
Figure 24-16 shows three point charges held in fixed positions by forces that are not shown. What is the electric potential energy U of this system of charges? Assume that d=12 cm and that
1. The drawing shows three possibilities for the potentials at two points, A and B. In each case, the same positive charge is moved from A to B. In which case, if any, is the most work done on the positive charge by the electric force? Account for your answer.
2. The electric field at a single location is zero. Does this fact necessarily mean that the electric potential at the same place is zero? Use a spot on the line between two identical point charges as an example to support your reasoning.
3. The potential is constant throughout a given region of space. Is the electric field zero or nonzero in this region? Explain.
4. In a region of space where the electric field is constant everywhere, is the potential constant everywhere? Account for your answer.
5. A positive test charge is placed in an electric field. In what direction should the charge be moved relative to the field, such that the charge experiences a constant electric potential? Explain.
6. The potential at a point in space has a certain value, which is not zero. Is the electric potential energy the same for every charge that is placed at that point? Give your reasoning.