Slide 1 / 154 Slide 2 / 154 Electric Potential and Capacitors www.njctl.org Slide 3 / 154 Slide 4 / 154 How to Use this File Each topic is composed of brief direct instruction · There are formative assessment questions after every topic · denoted by black text and a number in the upper left. Electric > Students work in groups to solve these problems but use student responders to enter their own answers. Potential and > Designed for SMART Response PE student response Capacitors systems. > Use only as many questions as necessary for a sufficient number of students to learn a topic. Full information on how to teach with NJCTL courses can be · www.njctl.org found at njctl.org/courses/teaching methods Slide 5 / 154 Slide 6 / 154 Electric Potential and Capacitors Click on the topic to go to that section Electric Potential Electric Potential Energy · Energy Electric Potential (Voltage) · Electric Potential due to a Uniform Electric Field · Capacitance and Capacitors · Return to Table of Contents
Slide 7 / 154 Slide 8 / 154 Electric Potential Energy Work and Potential Energy q+ q+ Q+ Q+ Recall that Work is defined as: Start with two like charges initially at rest, with Q at the origin, and q at infinity. To calculate the work needed to bring q from infinity, until it is a distance r from Q, we need to use calculus, because of the non In order to move q towards Q, a force opposite to the Coulomb constant force. Then, use the relationship: repulsive force (like charges repel) needs to be applied. Assume that the potential energy of the Q-q system is zero at infinity, and adding up the incremental force times the distance between the charges at each point, we find that the Electric Potential Energy, U E is: Note that this force is constantly increasing as q gets closer to Q, since it depends on the distance between the charges, r, and r is decreasing. Slide 9 / 154 Slide 10 / 154 Electric Potential Energy Electric Potential Energy This is the equation for the potential energy due to two point Again, just like in Gravitational Potential Energy, Electric Potential charges separated by a distance r. Energy requires a system - it is not a property of just one object. In this case, we have a system of two charges, Q and q. Another way to define the system is by assuming that the magnitude of Q is much greater than the magnitude of q, thus, the This process summarized on the previous page is similar to how Electric Field generated by Q is also much greater than the field Gravitational Potential Energy was developed. generated by q (which may be ignored). The benefit of using Electric Potential Energy instead of the Now we have a field-charge system, and the Electric Potential Electrical Force is that energy is a scalar, and calculations are energy is a measure of the interaction between the field and the much simpler. There is no direction, but the sign matters. charge, q. Slide 11 / 154 Slide 12 / 154 Electric Potential Energy Electric Potential Energy What is this Electric Potential Energy? q- Q+ It tells you how much energy is stored by work being done on the system, and is now available to return that energy in a different form, such as kinetic energy. Again, just like the case of If you have a positive charge and a negative charge near each Gravitational Potential Energy. other, you will have a negative potential energy. If two positive charges are placed near each other, they are a system, and they have Electric Potential Energy. Once released, they will accelerate away from each other - turning potential energy into kinetic energy. These moving charges can now perform work on another system. This means that it takes work by an external agent to keep them from getting closer together.
Slide 13 / 154 Slide 14 / 154 Electric Potential Energy 1 Compute the potential energy of the two charges in the following configuration: +Q 2 +Q 1 Q+ q+ 8 9 10 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 q- Q- A positive charge, Q 1 = 5.00 mC is located at x 1 = -8.00 m, and a positive charge Q 2 = 2.50 mC is located at x 2 = 3.00 m. If you have two positive charges or two negative charges, there will be a positive potential energy. This means that it takes work by an external agent to keep them from flying apart. Slide 14 (Answer) / 154 Slide 15 / 154 2 Compute the potential energy of the two charges in the 1 Compute the potential energy of the two charges in the following configuration: following configuration: +Q 2 -Q 1 +Q 2 +Q 1 10 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 A negative charge, Q 1 = -3.00 mC is located at x 1 = -6.00 m, Answer A positive charge, Q 1 = 5.00 mC is located at x 1 = -8.00 m, and and a positive charge Q 2 = 4.50 mC is located at x 2 = 5.00 m. a positive charge Q 2 = 2.50 mC is located at x 2 = 3.00 m. [This object is a pull tab] Slide 15 (Answer) / 154 Slide 16 / 154 3 Compute the potential energy of the two charges in the following configuration: -Q 2 -Q 1 10 -10 -10 -9 -9 -8 -8 -7 -7 -6 -6 -5 -5 -4 -4 -3 -3 -2 -2 -1 -1 0 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 A negative charge, Q 1 = -3.00 mC is located at x 1 = -6.00 m, A negative charge, Q 1 = -3.00 mC is located at x 1 = -6.00 m, and a negative charge Q 2 = -2.50 mC is located at x 2 = 7.00 m. and a negative charge Q 2 = -2.50 mC is located at x 2 = 7.00 m.
Slide 16 (Answer) / 154 Slide 17 / 154 4 A student is given the below values for a system of charges. What 3 Compute the potential energy of the two charges in the can the student say about this configuration? Select two following configuration: answers. -Q 2 -Q 1 8 9 10 10 -10 -10 -9 -9 -8 -8 -7 -7 -6 -6 -5 -5 -4 -4 -3 -3 -2 -2 -1 -1 0 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 9 A negative charge, Q 1 = -3.00 mC is located at x 1 = -6.00 m, A negative charge, Q 1 = -3.00 mC is located at x 1 = -6.00 m, A An external force must act on the charges to prevent them from and a negative charge Q 2 = -2.50 mC is located at x 2 = 7.00 m. and a negative charge Q 2 = -2.50 mC is located at x 2 = 7.00 m. moving apart. Answer B An external force must act on the charges to prevent them from getting closer together. C Decreasing the distance between the two charges increases the electric potential energy of the system of charges. D Substituting each charge with the same value, but opposite signs (positive to negative, negative to positive) will have no effect on the calculated electric potential energy. [This object is a pull tab] Slide 17 (Answer) / 154 Slide 18 / 154 Electric Potential Energy of 4 A student is given the below values for a system of charges. What can the student say about this configuration? Select two Multiple Charges answers. To get the total energy for multiple charges, you must first find the energy due to each pair of charges. Answer Then, you can add these energies together. Since energy is a scalar, B, D A An external force must act on the charges to prevent them from there is no direction involved - but, there is a positive or moving apart. negative sign associated with each energy pair. B An external force must act on the charges to prevent them from For example, if there are three charges, the total potential energy is: getting closer together. C Decreasing the distance between the two charges increases the [This object is a pull tab] electric potential energy of the system of charges. D Substituting each charge with the same value, but opposite signs (positive to negative, negative to positive) will have no effect on Where U xy is the Potential Energy of charges x and y. the calculated electric potential energy. Slide 19 / 154 Slide 20 / 154 Electric Potential Energy of Electric Potential Energy of Multiple Charges Multiple Charges Let's compute the electric potential energy of the three q 2 q 2 charge configuration to the right. There are no values for the distances q 1 q 1 between the charges or for the charges. So, we're looking for an algebraic solution. q 3 q 3 Quick notation review: r 12 means It's that easy! That's why you should always solve the distance between charges physics problems algebraically first - it shows you 1 and 2. understand the concept. This general equation can be used to solve any configuration of three charges - Here's the equation we're going to use: you just need to plug in the values. The k was factored out so you only have to multiply by it one time. Saves calculations and reduces errors. Try this within your groups before going to the next slide.
Slide 21 / 154 Slide 22 / 154 Slide 23 / 154 Slide 23 (Answer) / 154 5 Compute the potential energy of the three charges in the following configuration: +Q 3 +Q 1 -Q 2 10 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 A positive charge, Q 1 = 5.00 mC is located at x 1 = -8.00 m, a negative charge Q 2 = -4.50 mC is located at x 2 = -3.00 m, and a positive charge Q 3 = 2.50 mC is located at x 3 = 3.00 m. Slide 24 / 154 Slide 24 (Answer) / 154 6 Compute the Electric Potential energy of the three 6 Compute the Electric Potential energy of the three charges in the following configuration. charges in the following configuration. q 1 = 4.2 μC q 1 = 4.2 μC q 2 = 3.6 μC q 2 = 3.6 μC q 1 q 1 q 3 = -5.2 μC q 3 = -5.2 μC r 12 = 0.034 m r 12 = 0.034 m q 3 q 3 r 23 = 0.039 m r 23 = 0.039 m r 13 = 0.072 m r 13 = 0.072 m Answer q 2 q 2 [This object is a pull tab]
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