ELS - Electric Potential
Electric Potential
Introduction
Just as a mass above Earth has some gravitational potential energy, an electric charge in an electric field has electric potential energy. Consider a positive test charge placed in a uniform electric field between two parallel plates. When placed near the positive plate, the charge has a relatively high electric potential energy. If moved near the negative plate, the charge will have a relatively low electric potential energy. If the positive charge were released within the electric field, the field would apply a conservative force to the charge and do work accelerating it from a high to low position (positive plate to negative plate). From earlier physics studies you found that the work done by a conservative force will be given as:
W = -ΔU, where W represents the work and U represents the potential energy of the object.
To calculate work we can multiply the force acting on the object and the distance over which that force acts. In the case of a charged particle in a uniform electric field:
W = -ΔU, where W represents the work and U represents the potential energy of the object.
To calculate work we can multiply the force acting on the object and the distance over which that force acts. In the case of a charged particle in a uniform electric field:
W = Fd = qEd
Combining these two equations we can see how the work done by the uniform electric field causes a change in the potential energy of the charged test particle.
ΔU=-qEd
The potential energy of a positive test charge will increase when it is moved against the electric field. The potential energy of a negative test charge will increase when it is moved with the electric field.
Earlier we found it useful to define our electric field as the force per unit charge. Similarly we find it useful to define a new quantity electric potential as the electric potential energy per unit charge.
, where V represents electric potential. Since potential energy is dependent on where you set your zero value, absolute potential energy has no physical meaning. Rather, just like gravitational potential energy, the only useful measurement of electric potential energy is the change in the value. Calculating the change in electric potential energy per unit charge gives us the electric potential difference (or just potential difference):
, measured in units of volts (V) where 1 V = 1 J/C. Because it is measured in volts, potential difference is often referred to as voltage. If you want a specific value for potential, V, you must chose a point where V = 0 for reference. Often we chose something connected to the ground (Earth ground) to have zero potential. In other cases we might chose potential to be zero at a great distance, r=∞.
As we learned earlier, electric fields are defined by the force they provide to a small test charge. Since the field between two charged plates is constant, the force experienced by a test charge is also constant. This allows for easy calculation of the motion in addition to the changes in energy and potential of a charged particle released between two oppositely charged plates. A device like an old television set or computer monitor relies on this principle to accelerate electrons from the rear of the picture tube to the screen where the electrons strike the screen creating the picture.
Electric Potential and Potential Energy Practice
Suppose an electron in the picture tube of a television set is accelerated from rest through a potential difference of +5000 V. What is the speed of the electron as a result of this acceleration?
SOLUTION Links to an external site.
Relation Between Electric Field and Electric Potential
We have seen how both the electric field and electric potential affect a charged particle q. From these relationships we can see how the electric field is related to the electric potential.
W=-ΔU & ΔU = qΔV→W=-qΔV
since W = qEd
qEd = -qΔV
d is the distance, parallel to the field lines, between the two points we are measuring our potential difference. The negative sign shows that the direction of the E field is the direction of decreasing potential, V.
Electric Field and Voltage Practice
Two parallel plates are charged to produce a potential difference of 50 V. If the separation between the plates is 0.050 m, what is the magnitude of the electric field in the area between the plates?
SOLUTION Links to an external site.
Equipotential Lines
A powerful way to visualize electric potential is by drawing equipotential lines. Equipotential lines are drawn such that any point along the line has the same electric potential. To achieve this, equipotential lines must be drawn so they are perpendicular to the electric field in any point. Notice how the equipotential lines for a constant E field between parallel plates are themselves evenly spaced and parallel. When we draw equipotential lines around a point charge they create concentric circles. When you look at the equipotential lines of the electric dipole you can see how, mathematically, things become significantly more complicated when the electric field is not uniform. Equipotential lines are similar to the topographic lines you find on maps. Those contours represent lines of constant elevation. If you were to walk along a contour line you would never change elevation and, therefore, never change gravitational potential energy.
Electric Volts
When measuring the energy of large objects, the joule works just fine. However, it is a particularly large unit to work with when discussing the energy of subatomic particles, like electrons. To deal with the energies of small particles we often use a unit known as the electron-volt (eV). One electron-volt is the energy needed to move one electron through a potential difference of 1 V.
1 eV = 1.6 x 10-19 J.
Remember that this is not an SI unit, so when doing calculations with eV, you must convert to joules.
Electric Potential Due to Point Changes
We have shown that the electric field a distance r from source charge Q is given by:
We can see how the electric field would be zero at a distance or r = ∞. At infinity we can also say that the electric potential, V, = 0. Using calculus we can then show that the electric potential at a distance r from a point charge can be giving as:
Applications: If you are interested in finding the electric potential at a point due to multiple point charges, all you need to do is calculate the potential due to each charge at the point using the above equation and add the potentials together. If you want to calculate the work done to move a charge through an electric field due to a point charge, you can't just use W=Fd because the force isn't constant. Instead you would use the equation W=qΔV where you calculate the beginning and ending V using our new equation above.
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