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Electric Potential Note that potential and potential energy are different things. In a uniform gravitational field the change in gravitational potential associated with moving a distance r is given by: Vg g y , where y r sin represents distance moved vertically (up is positive). By analogy, write down the equivalent expression to represent the change in electric potential associated with moving a distance r in a uniform electric field: VE ________, where r sin represents the distance moved ____________________. V is known as “potential difference”, and is also often referred to as “voltage.” Potential difference is a lot like pressure. If there is a potential difference between two points then there is a tendency for charges to move from one point to another. Positive charges move toward lower potential (and lower potential energy). Negative charges move toward higher potential (this is also lower potential energy). Equipotentials: An equipotential line, or an equipotential surface, connects all points that have the same potential. What do the gravitational equipotential surfaces look like in this room? Equipotentials are always perpendicular to field lines. In fact, field lines point in the direction of the maximum decrease in potential. Two charges, +3Q and –Q, are separated by 4 cm. Are there any points along the line passing through them (and a finite distance from the charges) where the net electric potential is zero? If so, where? Are there points off the line, near the charges, where the net electric potential is zero? Consider the following two-dimensional situation. You place four charges in a square, with one charge at each corner. Each charge has a magnitude of Q, but you get to choose whether it is + or –. Each charge is a distance r from the center of the square. How many different arrangements of four charges are there? How many different values can you obtain for the electric potential at the center of the square? Figure out how many of the various arrangements of charges correspond to each of the possible values of the electric potential at the center, and draw some sketches to go with them. More Potential, and Capacitors Note that potential and potential energy are different things. Two charges, +3Q and –Q, are separated by 4 cm. The charges are on the x-axis, with the +3Q charge at x = -2 cm and the –Q charge at x = +2 cm. Ask a question involving force for this situation. Ask a question involving field for this situation. Ask a question involving field, and then a follow-up question involving force. Ask a question involving potential energy for this situation. Then re-phrase the question without using the word “potential” or the word “energy”. Ask a question involving potential for this situation. Ask a question involving potential, and then a follow-up question involving potential energy. A capacitor is a device for storing charge. A common example is a parallel-plate capacitor, which consists of two metal plates placed parallel to one another. The plates can be separated by air, vacuum, or an insulating material – a piece of insulating material in a capacitor is known as a dielectric. List any practical applications of capacitors that you are aware of. There are four basic equations we use for capacitors: 1. C V Q : The charge Q stored on a capacitor is proportional to V , the potential difference across the capacitor. C is the capacitance of the capacitor, which has units of farads (F). 2. Capacitance is a measure of how much charge a capacitor can store. It is determined solely by the geometry of the capacitor, and whether anything is between the capacitor A plates. For a parallel-plate capacitor the capacitance is given by: C 0 . d A is the area of each plate; d is the distance between the plates; is the dielectric constant, which is equal to 1 for vacuum and almost exactly 1 for air. 0 is the 0 permittivity of free space, and it is related to k. 1 2 1 4 k 1 2 8.85 1012 C2 / N m2 3. Energy stored in a capacitor is given by U C V Q V 2 1 Q2 . 2 C 4. We assume that parallel-plate capacitors have a uniform electric field, so the relationship between the electric field inside a capacitor and the potential difference across the capacitor is V E d . Capacitor problems are generally split into two kinds: 1. The capacitor is always connected to a battery or power supply that has a fixed potential difference. This ensures that the _________________________ is constant. When you make a change to the plate separation, dielectric constant, or plate area (that’s hardest to change) that changes the __________________________. Knowing what is going on with those two variables allows you to calculate ____________________________________________. 2. The capacitor is charged by first being connected to a battery or power supply, and then disconnected so it is isolated from everything. This ensures that the _________________________ is constant. When you make a change to the plate separation, dielectric constant, or plate area (that’s hardest to change) that changes the __________________________. Knowing what is going on with those two variables allows you to calculate ____________________________________________. More Capacitors Consider the situation of a parallel-plate capacitor. First, assume the plates are far apart. Connecting the capacitor to a battery causes, in effect, electrons to be pumped from one plate of the capacitor to the other. This gives a charge of –Q on one plate and +Q on the other, so we say that the capacitor stores a charge Q. The “electric pressure” the battery is working against is the repulsion of all the like charges on each plate. A particular battery can basically achieve a particular charge density on the plates, and then no more charge can be pumped. If we increase the area of the capacitor plates do you think more charge can be stored on the capacitor, or less? Why? If we now bring the capacitor plates close together the positive charge on one plate, and the negative charge on the other, experiences some attraction because of all this opposite charge in its vicinity. More charge can be stored on the plates in this case because the battery does not have to do everything itself – it gets some help from the charge on the other plate. Sketch the electric field between the plates of a capacitor. Usually we fill the space between the capacitor plates with insulating material, which we call dielectric material. The dielectric material gets polarized by the field in the capacitor, but the dielectric material does not allow charge to flow from one plate to the other. Sketch the electric field in the capacitor when the dielectric material is present. Now introduce a rectangular piece of metal between the plates (it can’t touch either plate!). Draw the field again. Can you see any disadvantages in using metal between the plates?