P-222_Salim_Lab 2

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The University of Tennessee, Knoxville *

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PHYS-250

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Physics

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Apr 3, 2024

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pdf

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Mustafa Salim muslim1@vols.utk.edu Lab Two Purpose: Investigate the relationship between electric field lines and equipotential surfaces. Through experimentation, we will examine scenarios where charged objects can move along surfaces without any work being done by the electric field, identifying and characterizing equipotential surfaces in the process. Activity One (a) The work W done on an object by a constant force is defined as W = F ∙ d . It is equal to the magnitude of the force, multiplied by the distance the object moves in the direction of the force. The SI unit of work is Nm = J. An object travels from point A to point B while two constant forces of equal magnitude are exerted on it, as shown in the figure on the right. ● Is the work done on the object by F 1 positive, negative, or zero? Why? - The negative work performed by F1 is evident in the line graph, illustrating its opposition to displacement. ● Is the work done on the object by F 2 positive, negative, or zero? Why? - The positive work carried out by F2 is evident in the line graph, indicating its alignment with or parallel to displacement. ● Is the net work done on the object positive, negative, or zero? Why? - -F1+F2=0. The overall work done amounts to zero. As previously explained, F1 is negative and F2 is positive, both with equal magnitudes. (b) An object travels from point A to point B while two constant forces of unequal magnitude are exerted on it, as shown in the figure on the right. ● Is the work done on the object by F 3 positive, negative, or zero? Why? - The work conducted by F3 is negative, as depicted in the line graph where it opposes displacement. ● Is the work done on the object by F 4 positive, negative, or zero? Why? - The work performed by F4 is positive, as indicated in the line graph where it aligns with displacement. ● Is the net work done on the object positive, negative, or zero? Why? - As long as the length corresponds to the vectors, the total work is negative, attributed to F3 being greater than F4. (c) A particle with charge +q e travels along a straight line from point W to point X. Is the work done by the electric field on the particle positive, negative, or zero? Explain using a sketch that shows the electric force on the particle and the displacement of the particle. - The positive work is a result of the charge moving in alignment with the electric field direction. (d) A particle travels from point X to point Z along the circular arc shown. ● Is the work done by the electric field on the particle positive, negative, or zero? Explain!

- The work performed on the particle is positive, as discerned from the trajectory it follows, being propelled outward by the field, forming an arc. (e) Suppose the moving charge in part (c) increases from +q e to +1.8 q e . ● Is the work done by the electric field as the particle travels from W to X greater than, less than, or equal to the work done by the electric field on the original particle. Explain! - With the magnitude of the positive charge increasing, it is anticipated that the work carried out by the field will also rise. ● How is the quantity "the work divided by the charge" affected by this change? - No change will occur, the quantity will remain the same. (f) The electric potential difference ∆V WX between two points W and X is defined to be the negative of the work done by the electric field on a charge q, divided by q, as q travels from W to X. ● Does this quantity depend on the magnitude of the charge that is used? Explain! - No, the quantity is independent of the charge magnitude of particles utilized for measurement. As the charge increases, so does the work, and the ratio remains constant. ● Does this quantity depend on the sign of the charge that is used? Explain! - No, the quantity is not dependent upon the charge's sign. If the charge shifts to negative, the work will similarly be negative, while the potential difference remains constant. When a net force does work on an object, its kinetic energy changes. W net = ½m(v f 2 - v i 2 ) = ∆K. (g) A particle of charge |q e | = 2*10 -6 C and mass m = 3*10 -8 kg is released from rest at point W. The speed of the particle is measured to be 25 m/s as it passes point X. ● Is q e positive or negative? Explain! - The value of qe is positive. The direction of the electric force aligns with the direction of the electric field. As the electric field direction is positive, so is the value of qe. ● What is the change in the kinetic energy of the particle as it travels from point W to point X? - 0.5*3*10^-8*40^2 = 2.4*10-5 J = 24 mJ ● Find the work done on the particle by the electric field between points W and X. - 2.4*10^-5 J ● What is the electric potential difference ∆V WX = V W - V X between points W and X? - change in K / qe = -2.40 / 2*10^-6 = -12 V (h) Assume you have a test charge at rest at a distance of 2 cm from the charge on the right. You want to move it. What path could you choose, so you would not have to do any work? What is the shape of the equipotential surface? (Remember that in general you can move in three dimensions.) Explain your reasoning . - Due to an equipotential surface being a sphere, the charge moving between points does zero work. (i) Find some equipotential surfaces for the charge configuration shown on the right, which consists of two charged metal plates placed parallel to each other.

What is the shape of the equipotential surfaces? Remember you are trying to decide how a test charge could move so that the electric field does no work on it. Sketch your predictions and explain your reasoning . - A vertically positioned rectangular plane would be perpendicular to the horizontal parallel lines and serve as the equipotential surface. * Picture is of both I and J* (j) Find some equipotential surfaces for the electric dipole charge configuration shown on the right. Sketch your predictions and explain your reasoning . - As you approach the charges and move away from the center, the equipotential surfaces become increasingly curved, resembling a cone in three dimensions. Activity Two (a) Start with just the one +10 nC charge at x = 13 m, y = 13 m. Describe the graphs. What do they tell you about the potential outside a uniformly charged sphere? Can you get information about the electric field outside a uniformly charged sphere from these graphs, i.e. can you draw field lines? Estimate the magnitude and direction of the electric field in units of V/m = N/C at x = 20 m, y = 13 m. - The graphs exhibit a cone shape, appearing to ascend to a particular maximum level where they plateau before descending again. When viewed from the top perspective, there are concentric circles extending outward. They indicate that the potential outside a uniformly charged sphere is lower than the potential at the center of the sphere. Yes, information about the electric field outside the sphere can be obtained. Its direction would be outward. (b) Now change the positions and magnitudes of your charges. Use the numbers below. Paste the upper graph into your word document. Describe both graphs. What do they tell you about the potential of this charge distribution? When observed from the side, this graph displays two peaks, with a raised central region between them. - When viewed from the top, it resembles two smaller sets of concentric circles within a larger concentric oval. This indicates that the charges are most concentrated at the two centers and diminish as you move outward. Additionally, the charges are uniformly positive.

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