It depends on where the zero reference for potential is. Though this might be unusual. Two very large metal plates are placed 2. Consider one plate to be at 12 V, and the other at 0 V. A very large sheet of insulating material has had an excess of electrons placed on it to a surface charge density of. Can you explain why without any calculations? Does the location of your reference point matter? A metallic sphere of radius 2. The metallic sphere stands on an insulated stand and is surrounded by a larger metallic spherical shell, of inner radius 5.
Now, a charge of is placed on the inside of the spherical shell, which spreads out uniformly on the inside surface of the shell. If potential is zero at infinity, what is the potential of a the spherical shell, b the sphere, c the space between the two, d inside the sphere, and e outside the shell?
Two large charged plates of charge density face each other at a separation of 5. A long cylinder of aluminum of radius R meters is charged so that it has a uniform charge per unit length on its surface of. Two parallel plates 10 cm on a side are given equal and opposite charges of magnitude The plates are 1.
What is the potential difference between the plates? The surface charge density on a long straight metallic pipe is. What is the electric potential outside and inside the pipe? Assume the pipe has a diameter of 2 a. Concentric conducting spherical shells carry charges Q and — Q , respectively.
The inner shell has negligible thickness. What is the potential difference between the shells? In the region , and E is zero elsewhere; hence, the potential difference is.
Shown below are two concentric spherical shells of negligible thicknesses and radii and The inner and outer shell carry net charges and respectively, where both and are positive.
What is the electric potential in the regions a b and c. A solid cylindrical conductor of radius a is surrounded by a concentric cylindrical shell of inner radius b. The solid cylinder and the shell carry charges Q and — Q , respectively. Assuming that the length L of both conductors is much greater than a or b , what is the potential difference between the two conductors?
From previous results , note that b is a very convenient location to define the zero level of potential:. Skip to content Electric Potential. Learning Objectives By the end of this section, you will be able to: Define equipotential surfaces and equipotential lines Explain the relationship between equipotential lines and electric field lines Map equipotential lines for one or two point charges Describe the potential of a conductor Compare and contrast equipotential lines and elevation lines on topographic maps.
An isolated point charge Q with its electric field lines in red and equipotential lines in black. The potential is the same along each equipotential line, meaning that no work is required to move a charge anywhere along one of those lines.
Work is needed to move a charge from one equipotential line to another. Equipotential lines are perpendicular to electric field lines in every case. For a three-dimensional version, explore the first media link. The electric field lines and equipotential lines for two equal but opposite charges. The equipotential lines can be drawn by making them perpendicular to the electric field lines, if those are known. Note that the potential is greatest most positive near the positive charge and least most negative near the negative charge.
Electric potential map of two opposite charges of equal magnitude on conducting spheres. The potential is negative near the negative charge and positive near the positive charge. A cross-section of the electric potential map of two opposite charges of equal magnitude. The electric field and equipotential lines between two metal plates. The distance between the plates is , so there will be between potential differences.
You have now seen a numerical calculation of the locations of equipotentials between two charged parallel plates. In Example 3. Given that a conducting sphere in electrostatic equilibrium is a spherical equipotential surface, we should expect that we could replace one of the surfaces in Example 3.
Inside will be rather different, however. To investigate this, consider the isolated conducting sphere of Figure 3. To find the electric field both inside and outside the sphere, note that the sphere is isolated, so its surface change distribution and the electric field of that distribution are spherically symmetric.
We can therefore represent the field as. Since is constant and on the sphere,. If , encloses the conductor so. As expected, in the region , the electric field due to a charge placed on an isolated conducting sphere of radius is identical to the electric field of a point charge located at the centre of the sphere.
To find the electric potential inside and outside the sphere, note that for the potential must be the same as that of an isolated point charge located at ,. For , , so is constant in this region. Since ,. The spheres are sufficiently separated so that each can be treated as if it were isolated aside from the wire. Note that the connection by the wire means that this entire system must be an equipotential. We have just seen that the electrical potential at the surface of an isolated, charged conducting sphere of radius is.
Now, the spheres are connected by a conductor and are therefore at the same potential; hence. The net charge on a conducting sphere and its surface charge density are related by. Substituting this equation into the previous one, we find. Obviously, two spheres connected by a thin wire do not constitute a typical conductor with a variable radius of curvature.
Nevertheless, this result does at least provide a qualitative idea of how charge density varies over the surface of a conductor. The equation indicates that where the radius of curvature is large points and in Figure 3. Similarly, the charges tend to be denser where the curvature of the surface is greater, as demonstrated by the charge distribution on oddly shaped metal Figure 3. The surface charge density is higher at locations with a small radius of curvature than at locations with a large radius of curvature.
A practical application of this phenomenon is the lightning rod , which is simply a grounded metal rod with a sharp end pointing upward. As positive charge accumulates in the ground due to a negatively charged cloud overhead, the electric field around the sharp point gets very large.
When the field reaches a value of approximately the dielectric strength of the air , the free ions in the air are accelerated to such high energies that their collisions with air molecules actually ionize the molecules. The resulting free electrons in the air then flow through the rod to Earth, thereby neutralizing some of the positive charge.
This keeps the electric field between the cloud and the ground from getting large enough to produce a lightning bolt in the region around the rod. An important application of electric fields and equipotential lines involves the heart. The heart relies on electrical signals to maintain its rhythm.
We can represent electric potentials voltages pictorially, just as we drew pictures to illustrate electric fields. Of course, the two are related. Consider Figure 1 , which shows an isolated positive point charge and its electric field lines. Electric field lines radiate out from a positive charge and terminate on negative charges. While we use blue arrows to represent the magnitude and direction of the electric field, we use green lines to represent places where the electric potential is constant.
These are called equipotential lines in two dimensions, or equipotential surfaces in three dimensions. The term equipotential is also used as a noun, referring to an equipotential line or surface.
An equipotential sphere is a circle in the two-dimensional view of Figure 1. Since the electric field lines point radially away from the charge, they are perpendicular to the equipotential lines.
It is important to note that equipotential lines are always perpendicular to electric field lines. Thus the work is. Work is zero if force is perpendicular to motion. More precisely, work is related to the electric field by. One of the rules for static electric fields and conductors is that the electric field must be perpendicular to the surface of any conductor.
This implies that a conductor is an equipotential surface in static situations. There can be no voltage difference across the surface of a conductor, or charges will flow.
One of the uses of this fact is that a conductor can be fixed at zero volts by connecting it to the earth with a good conductor—a process called grounding. An artificial pacemaker and a defibrillator can be used to initiate the rhythm of electrical signals. The equipotential lines around the heart, the thoracic region, and the axis of the heart are useful ways of monitoring the structure and functions of the heart. An electrocardiogram ECG measures the small electric signals being generated during the activity of the heart.
More about the relationship between electric fields and the heart is discussed in Energy Stored in Capacitors. Move point charges around on the playing field and then view the electric field, voltages, equipotential lines, and more. Figure 5. The electric field near two equal positive charges is directed away from each of the charges. Figure 9. A charged insulating rod such as might be used in a classroom demonstration. Figure Skip to main content.
Electric Potential and Electric Field. Search for:. Equipotential Lines Learning Objectives By the end of this section, you will be able to: Explain equipotential lines and equipotential surfaces. Describe the action of grounding an electrical appliance. Compare electric field and equipotential lines. Grounding A conductor can be fixed at zero volts by connecting it to the earth with a good conductor—a process called grounding.
PhET Explorations: Charges and Fields Move point charges around on the playing field and then view the electric field, voltages, equipotential lines, and more. Click to run the simulation. Conceptual Questions What is an equipotential line?
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