PHYS 2126 Fall 2024 Potential Mapping Lab Report 2 Corrected

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University of Houston**We aren't endorsed by this school

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PHYS 2126

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Electrical Engineering

Date

Dec 26, 2024

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Uploaded by BrigadierReindeer2016

/ NAM LAB PARTNERS Instructor b %cz%m Potential Mapping ' Experiment 2 INTRODUCTION Electric potential is a very important concept in electrostatics. It is usually easier to use because it is a scalar, whereas Coulomb forces and electric fields are vectors. In this experiment, you will measure the potential surrounding a charged body to create a two-dimensional representation of the potential and use our findings to obtain the electric field. THEORY The electric potential of point charge @ is given by V=k Sz A (1) T / where 7 is the distance measured from the position of the charge. As we move away from the ‘D charge, the electric potential decreases and reaches a value V = 0 at T = infinity. In Figure 2.1, the electric potential at point A is greater than at point B since it is closer to the charge Q. On the other hand, since points A and C are at the same distance from @, V, = V. If instead, we have a system where there are 2 or more charges, the electric potential at any point in space is given by the algebraic (not vector) sum of the potential due to each individual charge. eennne Lot ey, o ., . ., o ., o e, o *, o s, o wee 0 POLLLLLAL TN s, K o ., s, o o s N N . i . : H H 5 ) 0 0 ) " s, tF;:gull-le 2.1: Equipotential lines for a positive point charge Q. The value of V decreases as we move away from e charge. An equipotential plot can help us visualize how the electric potential changes in space. These plotg are 2 dimensional and consist of a set of equipotential lines. An equipotential line is formed by simply connecting all points that share the same electric potential value. In F igure 2.1, for - g example, equipotential lines will form concentric circles with Q at the center.

The electric field is another important concept in electrostatics. s Tlasy lteoctrlr.liipfitzlede;:e cltsng field lines using the equipotential lines. Unlike the electrlc.pOteﬂtla_l, the ¢ e o vector quantity; it has magnitude and direction. The electng fielq 1S glVenl }t, feld cgn b electric potential divided by the change in position. In one dimension, the electric written as AV Ax’ where the negative sign simply gives the direction of the field. Therefore, the closer equ.ipot.entlal lines are spaced, the larger the magnitude of E in that region. Electric field lines point in t?le direction of decreasing electric potential, and they are always perpendicular to the equipotential lines. In this experiment, we will apply a voltage to the electrodes in a slightly conductive piece of paper and measure the electric potential across its surface. Because the paper does have a finite resistance, a small current will propagate on its surface creating-a potential difference. Since the current does not change with time the potential will not change either, and we can use a multimeter to measure V on the surface and create a two-dimensional map of the potential. EXPERIMENT NO. 2 1. Connect the power supply to the electrodes on the paper as shown in the diagram in Figure 2.2. Use push pins to fix the ring connector wires to the electrodes on one end and alligator clips (arrows in the diagram) on the other end to connect the power supply. Power Supply (NWERNREANSNRBANAN AN AN E N TR aNaN FEE OO AR B e e e Buiekngs .:iiiil.:,tg: o 7 il ' B x‘ E“E Dh ‘gh w‘lj -"“i - R FrE R AT B T 0 T :;;p-pu;‘;dg-ﬂ‘ T R T s @ RN R asaifasaasy. @ (aRa)s EEE. gt pE;- H LR DR R Ere SRR ~ G ¥ SRaEERLENRLES fi—~§Hé fié 0 R FE R e O e R B R h%mﬂhhhmﬂm’ugm BH Figure 2.2: Potential mapping — experimental setup

2. One end of the digital multimeter (DMM) is connected to the ground input of the power Supply.. The. ground is simply the reference voltage value against which all measurements will be made; in this case, Vyrouna = 0.00 volts. The other end of the DMM is placed at whatever point on the paper you want to measure V. To get the exact location, you must place this end vertically on the paper. 3. Turn ON the power supply. Each side should provide 5.00 V. To check that the push pins make good contact, use the DMM to read the potential at each electrode. The potential on one electrode should read +5.00 V and —5.00 V on the other. Take reading at different points on the electrode to convince yourself that it is the same. The electrodes have been drawn with silver ink, which has a much larger conductivity than the paper. + 4.37F A g8 4 4. You now want to start creating the equipotential lines. Use the DMM to find a location where the potential is 3.00 volts and mark that position on paper provided to sketch the equipotential map. Continue to identify other locations with ¥V = 3.00V. To have a clear picture, these locations should not be more that 2.00 cm apart. Connect the dots with a soft curve to obtain the equipotential line for V = 3.00 V. 5. Similarly, sketch the equipotential lines for V = 1.00V, 0.00V, —1.00V, —3.00 V. 6. After you have finished drawing the equipotential lines, draw the electric field lines. Remember that these lines are perpendicular to the equipotential lines, and they point in the direction of decreasing V. Be sure to illustrate the direction of E in your plot and to clearly label each set of lines. 7. The configuration of two straight electrodes is similar to that of a parallel plate capacitor. Starting on one plate, take several measurements of V spaced by 1.00 cm until you reach the other plate. Take the measurements along the middle of the plates. Table 2.1: Parallel Plate Capacitor - Potential versus Distance V (volts) X (cm) SV Hv 2.8V e\ -1V OV -0.1V =), 3N -2.9V Al Y] *H 6V = lon |t~ E|n || —|O o 8. Plot your results in a V versus x graph and calculate the electric fielg‘between the plates. Show all calculations on the graph paper provided. i / \Q& 9 [ &

QUESTIONS t each other? Explain. )e value an mofe, + wo 1. Can two or more equipotential lines intersec No- if such lines crossed, then }key would not hWave a $19 The piind 0% which 4\‘\47 Would cross would im&rca}e 3 eo:n’r with o\:”uu\f s:mul'}av\eoos poj(en-}'.a\ Va]uggl (Qm}u;na -H,c ".V\Ls Js erroneovs 2. The graph shown below can be divided into 5 different segments. ) In which segmen(:(s) glol you expect to have the largest magnitude for the electric field? b) In which segment(s) do y expect to have the smallest magnitude for the electric field? Explain your answers. C) Calculate the magnitude of the electric field for each segment. 8.00 V (volts) ) 50 100 150 200 250 30.0 350 40.0 450 500 550 60.0 —A —i—g XG0 - p —f ~A 3) L-dimengrons) cleckic feld @ E= —fi- , o dhe slope of the line will indicate dhe maf)h;’(\ule of the eleckic field, Seqmants A ond E hse the skeepest slope , so these will contarn the \araeg-l' electrc field Maan:}uJe b) vsmg M, 1o J The logec &LOVC, Segnent D 7s Ha-b with 3 slope ot zeco, so o il Cov\-bm the small¢,5+ Qledr:c f:g]J Maan:hJe ¢) ___L g B C | D ; L T kel Y Lo 4 A pr 3. 3 N (0 P Dlae e X S po g WG oAy ghplitas lhy gt i L s eial Z -0\ Ven \a ) Zirse - 16 cM =0.06 V Slope 22€¢0 . 2 0.2 N/em N o e T - 02 Njem Z6.67VmM a0 L

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