Electric Potential A New Physical Quantity

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Leo Preston
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1 Electric Potential A New Physical Quantity 1.1 Represent and Reason A positive test charged object is placed at each of the following points (A through F) near a source charged object. a) Rank the potential energies for the system test charge-source charge from greatest to least (for points A-C). (Remember: a large negative number is less than a small negative number.) Show at least one additional point where you can place a test charge so that the electrical potential energy is the same as for the configuration for point C. A B C b) Rank from greatest to least the potential energies of the system test charge-source charge shown below (D-F). Show at least one additional point where you can place a test charge so that the electrical potential energy is the same as for the configuration for point E. D E F + c) How might the magnitude of the potential energy depend on the magnitude of the source charge? How is the magnitude dependent on the distance from the source? d) Does a system have potential energy if it has only one charged object? e) Recall and transcribe the mathematical model for electrical potential energy. How does electric potential energy depend on the source charge? On the test charge? f) Think of how you can define an energy-type quantity that will characterize the electric field from the energy perspective similarly to how the quantity of E field characterizes the field from the force-type perspective.

2 Did You Know? Electrical potential V due to point-source-charged objects: The electrical potential field (V field) at a point A can be defined in a way that is similar to the E field. In both cases a charge, several charged objects, or a distribution of charged objects, create the field. The figure on the right considers a simple situation: two charged objects q 1 and q 2 are the sources of the electric field. We place a small test charge at point A. The electric potential V at point A due to these sourcecharged objects equals the net electric potential energy of a system that encompasses the sourcecharged objects along with the test object placed at A divided by the charge of the test object. The electric potential at A is then: A + - q1 +q q2 - q U qsorce and U qsource1qtest + U qsource2qtest +... If the electric field is created by one source object, then the electric potential energy of interaction of a source-test charged objects is U e k q source r the test object we have:. Dividing by the charge of kq i i r itoa Where the summation is for all charges and r i to A is the distance from source charge i to point A. This is algebraic addition but you must include the signs of the source charged objects. For the figure shown above, the electric potential at point A is: k( q) r q to A + k(+q) r +q to A (It is assumed that the electric potential energy and the electric potential are zero when the test charge is infinitely far from A.)

3 1.2 Reason a) Why is the test charge present in the definition of the V field even though the V field characterizes the field, not the test object? b) How is the definition U qsorce and U qsource1qtest + U qsource2qtest +... similar to the definition of E field E A F qsource on i? How is it different? c) Think of the analogy of the V field quantity in the gravitational field. Where is the largest gravitational potential? The smallest? Where did you choose the zero location? 1.3 Represent and Reason a) Draw a positive charge of 9 nc at the center of a white board (or sheet of paper) and find locations of 5 points such that: V B V c > V D > V E. b) Then measure the distance to those points with a ruler and calculate the actual values of the potential at those locations. Where did you choose the zero potential to be? c) Draw two graphs, one under the other, for the 9 nc charge: E versus r and V versus r. How are the graphs similar? How are they different?

4 1.4 Regular Problem Two charged objects are shown (their charges are +5 x 10-3 C and -3 x 10-3 C. Determine the electric potential V at point A. Specify your choice of the reference point where the potential is zero. Then determine the electric potential energy of the system if an additional +3 x 10-3 C charge is placed at 0.9 m. x1 0 x2 0.4 m xa 1.2 m + x- axis a) Explain what would happen to the electric potential if point A were at x 0.8 m. b) Explain what would happen to the electric potential energy of the system if an object of +3 x 10-3 C were placed at that point (x 0.8 m). c) How would the electric potential be affected if point A were an infinite distance away? d) What would this mean for the electric potential energy for the same system if a +3 x 10-3 C were placed an infinite distance away? e) Imagine placing a small positive test charge at point A in the original scenario. What will happen to it? Now, what will happen to a negatively charged object placed at the same point? Explain. 1.5 Check for Understanding Below, two equally charged objects are fixed in space at the locations (dots) shown. Points ( s) in the area around these objects are labeled a h. Rank the electric potential of the points below; explain your rankings. e - Q a c f b d g +Q h

5 1.6 Represent and Reason The same situation is represented in different ways in the table below. Are the representations consistent with each other? Explain. Words Sketch Determine the electric field E and electric potential V at a distance a above a point directly between an electric dipole, which consists of an object of charge +Q on the left and a second object of charge Q a distance a to the right. y. E, V? + +Q Q x a/2 a/2 a Mathematical representation and solution V k(+q) [( a 2 )2 + a 2 ] 1/2 + k( Q) [( a 2 )2 + a 2 ] 1/ Regular Problem A +5.0 nc charged object is at rest at the origin. Determine the potential V field at the following locations: x 0.5 m, x 1.0 m, x 2.0 m, x 3.0 m, x 5.0 m, and x 10.0 m. What would the values be for points along the y-axis? 1.8 Regular Problem A charged object +q is placed at the origin and a second charged object of +3q is placed 1.0 m away along the x-axis. Determine the location where the E field is zero. Determine the location where the electric potential is zero. Are they the same location? Explain. 1.9 Regular Problem Two charged objects lie along the x-axis. The object at the origin is q µc. The second object q µc is placed a certain distance away such that the potential energy the system of charged objects possesses is J. Determine their separation Regular Problem In the Bohr model of the hydrogen atom, a negatively charged electron orbits a proton. If the electric potential energy associated with the electron and proton is -4.35x10-18 J, what is the distance between the two charged objects?

Introduction to Charges. BCLN PHYSICS 12 - Rev. Sept/2012

Introduction to Charges. BCLN PHYSICS 12 - Rev. Sept/2012 Electrostatics ~ Learning Guide Name: Instructions: Using a pencil, answer the following questions. The Pre-Reading is marked, based on effort, completeness, and neatness (not accuracy). The rest of the