Electric field and Electric potential

Electricfield and Electric potential

Sectionnumber

Abstract

Electricfield and electric potential can be used to determine thequantitative and qualitative aspects of potential difference. It isbased on this theoretic deduction that this experiment was conducted.It was carried out to determine the qualitative and quantitativeaspects of potential difference. The experiment had involvedarranging four sensors at equal distance in the vertical andhorizontal distance. The objective of the experiment was to exploreelectric field and potential different.

Atmajor grid distances, that is, 0.5m 1.0m 1.5m 2.0m and 2.5themagnitude of the potentials were as follows 1.5V 3.0V 4.5V 7.0Vand 10.0V. The values of the potentials were plotted against themajor grid distances on a graph in excel to identify the error andaccuracy of the experiment. Furthermore, the potential difference wasplotted against the inverse of the radius (r) to determine thequalitative aspect of the experiment.

Samplecalculations were carried out using the experimental data and acombination of formulas from the theory of the electric field andelectric potential. Discussion and analysis of the graphs obtainedwas carried. The analysis of the results was compared with theexpected result.

Objectives

Theobjectives of the experiment were as follows:

  • To explore electric field around different configurations of charges and map their electric fields and equipotential lines.

  • To explore the behavior of charged pith ball suspended in a uniform electric field of parallel plates.

  • To experimentally determine the strength of the electric field and potential difference between two oppositely charged parallel plates.

  • To determine the magnitude and direction of the force on a charged particle in an electric field.

Procedure

PartI a. Electric field of the point charge distribution.

Foursensors were arranged around the charge at equal distance, that is,two in the vertical axis and two on the horizontal axis. The valuesof the length of the vectors were compared. The observation wasexplained qualitatively. Electric field was calculated using equationthree of the calibration. Average value from all of the sensorsreading was computed and it was further compared with the calculatedvalue. Comparison for the E-field readings at 0.5m and 1.0m from thesource charge was done. Moreover, the readings were compared with thesensors values.

PartI b. Electric potentials and equipotential lines of point charge

Thevalues of potentials at 12345 and major grid distances(0.5m1.0m1.5m2.0m2.5m) were measured and recorded. The distanceswere taken in two directional radii, that is, horizontal andvertical. Two graphs were made from the results (potential Vavevs. distance r and Vavevs. inverse of distance). The experiment was then repeated withnegative charge.

PartI c. Electric field, potential and equipotential lines of electricdipole

Fiveclosed equipotential lines of magnitudes 1.5V 3.0V 4.5V 7.0V and1.0V around each charge were generated. Orientation comparison of theelectrical field vectors was carried out.

PartII a. Electric field and electric potential between parallel plates

Usingthe apparatus used in the coulomb law lab, a high voltage DC supplywas used to put equal, but opposite charges on a two parallel plates.It was assumed that the plates are closed and large enough to providea constant electric field in the region occupied by the pith ball.Similarly, as it was done in the Coulombs lab, the pith ball was alsocharged with charging rods. The ball was continuously charged on therod by rubbing it alongside the charging cat. Rubbing of the pithball was continuous until a charge equal to 120 was observed. At thispoint the pith balls were still neutral. In order to transfer part ofthe excess charge from the ball on the charge rod to the two neutralballs, the rod with the fully charged ball was drag to the middle ofthe neutral balls. A couple of back and forth swings was carried.Afterwards, the pith balls were fully charged each having a charge of6.168e-9 C. the power supply in the experiment was being controlledby a knob which rotates at 270 degrees. From the experiment it wasnoticed that, one of the extreme dot on the knob matches with one ofthe markers in the body of the voltage supplier.

PartII b. Charging rod with charge # = 100

Theexperiment was repeated using a charging rod of charge # =100. Thedeflection angle θof the pith ball was measured using a protractor. The maximum voltageof the power supply was calculated from the equilibrium condition andit was compared with the value found from part I b experiment.

Experimentaldata

S

Radius (meters)

Potential difference(voltage)

1

0.5

1.5

2

1.0

3.0

3

1.5

4.5

4

2.0

7.0

5

2.5

10.0

Maximumcharge # = 120

Pithball mass mb = 0.050 (grams),

Chargeon each ball = 6.168e-9 C

Rotationof the knob = 270 degrees

Minimumcharge # = 100

Deflectionangle = 8˚

Results(sample calculations)

E= F / q0

F= k |q·q0| /r2

E= k |q| / r2

Thefield has a (1/r2)

ΔPE= PEf– PEi= – Ws

V= W / q0

Theunit of potential is defined to be volt, 1V=1 J/C(jouleper coulomb).

E=ΔV/Δr

±1 nC

Charge# = 100 charge on each ball = 4.692e-9 C.

1/r

Potential difference

2

1.5

1

3.0

0.66667

4.5

0.5

7.0

0.4

10.0

Maximumvalue of E is given by,

E= k |q| / r2

Takingr = 2.5m

Andk=8.99×109N·m2/C2.

Andq = 120C

E= (8.99×109x120)/(2.52)

=1.72608 x 1011N/C

Thevalue of Force is given by the formula

F= k |q·q0| /r2

F= (8.99×109x120 x100)/(2.52)

=1.72608 x 1013

ΔPE= PEf– PEi= – Ws

ΔPE= 10.0 – 1.5

=8.5 V

ThusW = -8.5 J

V= W / q0

V= 8.5/120

=0.0708333 J/C

E=ΔV/Δr

E=(3.0 – 1.5)/ (1 – 0.5)

=1.5/0.5

=3

Discussionand Analysis

Principleof superposition is the law that the resultant of comparable vectormagnitudes at a point is a function of the sum of the individualmagnitudes, especially the law that the displacement at a point in amedium undergoing simple harmonic motion is equal to the sum of thedisplacements of each individual wave.

Fromthe theory of electric field and electric potential, the relationshipbetween the two is given by the expression as follows: E=ΔV/Δr

Thisvalue of Ewaseasily calculated from the gradient of the graph, therefore, thetheory correctly describe the phenomena being tested.

Fromthe experiment the results obtained were quantitative in that thevalues of potential difference were measured up to 10.0v. The firstgraph drawn was a straight line indicating the qualitative aspect ofthe experiment. When the potential difference was plotted against theinverse of radius, it was difficult to come up with a straight linegraph. The only option was to draw line of best fit, hence thequalitative analysis of the result. There were some errorsexperienced during the experiment. Sources of the errors include:

  1. Parallax error

  2. Vibration of the apparatus

  3. Change of environment

Conclusion

Inconclusion, the experiment was successful in that the objective ofthe experiment was achieved. Moreover, the knowledge of superpositionwas well understood. However, the result obtained was a little bitdifferent from the expected result. This was due to some errorsencountered during the experiment.

Electric Field and Electric Potential

ElectricField and Electric Potential

Sectionnumber

Abstract

Whenthe electric potential or voltage is delivered by any number of pointcharges can be computed from the expression (Voltage = k x) by basicexpansion since voltage is a scalar amount. The potential from apersistent distribution can be acquired by summing the commitmentsfrom every point in the source charge. The computation of potentialis characteristically less difficult than the vector total obligedascertaining the electric field.

ElectricField and Electric Potential can be utilized to focus thequantitative and subjective parts of potential distinction. It istaking into account this theoretic derivation that this trial wasdirected. It was completed to focus the subjective and quantitativeparts of potential contrast. The main goal of the analysis that wasto be performed was to investigate the electric field and thepotential different. A point charge is an item like a charged ballthat is very little. Such protests will eventually add to both theelectric field and the electric potential in the space all aroundthem. The commitment of an object of charge Q to the electricpotential at a point a separation r away is given by: V=kQ/r

Objectives

-Examine electric fields around diverse arrangements of charges andguide their electric fields together with the equipotential lines.

-Examine the conduct of a charged essence ball which will be suspendedalong the same uniform electric-field which comes from parallelplates.

-Do an experiment that focuses on the quality of an electric fieldtogether with potential difference or contrast that will occurbetween two parallel plates which are oppositely charged.

-Find out the size as well as the direction of the power on a chargedmolecule along electric field.

Procedureand Experimental data

PartI a. Electric field of the point charge distributions

Makean Electric Grid and bring in a +ve point charge to the intersectionmatrix at the focal point of the particular screen. You will seebolts drastically leaving the point of charge. Electric field linesare nonexistent smooth lines joining the directional bolts. Bring inan &quotE-Field Sensor&quot to the screen all around the existentpoint charge this will enable me to see the extent and the course(direction) of the field anytime. You will be able to find that thesize of electric field increases once the sensor moves closer to thecharge: when a bolt which stands for the magnitude and courses of theelectric field starts getting longer it shows that the electric fieldis stronger.

PartI b. Electric potentials and equipotential lines of point charge

Makean Electric Grid and bring in a +ve point charge to the intersectionmatrix at the focal point of the particular screen. Click the meterthat has the focus and thereafter move it around to gauge thepotential of charge. Position the focus at different lengths from theparticular positive charge while you click on &quotPlot&quot. Thiswill create an equipotential line all through that particular point.Measure and also make records of the estimations of thepossibilities at 1 2 3 4 5 noteworthy distances (0.5 m 1.0 m1.5 m 2.0 m 2,5 m) from the flat and vertical.

PartI c. Electric field, potential and equipotential lines of electricdipole

Makean Electric Grid and bring in a +ve and –ve point charge to theintersection matrix at the focal point of the particular screenleaving it a distance of 2 meters. This type of configuration iscommonly referred to as the electric dipole. Generate 5 focus linesthat will be around the charge and will have specific magnitudes of1.5 V 3.0 V 4.5 V 7.0 V and 10 V.

PartII a. Electric field and electric potential between parallel plates

Ahigh voltage will be used with opposite charges on two parallelplates. An assumption will be made in reference how close and largethe individual plates should be in reference to the electric fieldprovided. The field will have a description of green arrows that willmove from the positive plate to the negative. Start up what is knownas the “Coulomb`s Law” apparatus, at this point one should chargethe balls with the rods for charging. When in the box you will seethe value of balls in mass to be 0.050 grams, charge # = 0 and thecharge on the ball used at = 0 C (zero Coulomb) – then it isdescribed as neutral.

Charge&nbsp+q1&nbspisat&nbsp(0,0)&nbspand&nbsp+q2&nbspat&nbsp(5,0).&nbsp The force of&nbsp+q1&nbspon&nbsp+q2&nbsppoints(a) West.&nbsp ( b) East.&nbsp (c)&nbsp North.

Charge&nbsp+q1&nbspisat&nbsp(0,0)&nbspand&nbsp+q2&nbspat&nbsp(5,0).&nbsp The force of&nbsp+q2&nbspon&nbsp+q1&nbsppoints(a) West.&nbsp ( b) East.&nbsp (c)&nbsp North.

Charge&nbsp+q1&nbspisat (0,0) and&nbsp+q2&nbspat&nbsp(0,-4).&nbsp&nbsp The force of&nbsp&nbsp&nbsp+q1&nbspon&nbsp+q2&nbsp&nbsppoints(a) South.&nbsp ( b) East.&nbsp (c) North.

Charge&nbsp+q1&nbspisat (0,0) and&nbsp+q2&nbspat&nbsp(0,-4).&nbsp&nbsp The force of&nbsp&nbsp&nbsp+q2&nbspon&nbsp+q1&nbsp&nbsppoints(a) South.&nbsp ( b) East.&nbsp (c) North.

Charge&nbsp-q1&nbspisat (0,0) and&nbsp+q2&nbspat&nbsp(-4, 0).&nbsp The force of&nbsp&nbsp-q1&nbspon&nbsp+q2&nbsp&nbsppoints(a) South.&nbsp ( b) East.&nbsp (c) West.&nbsp&nbsp&nbsp

Charge&nbsp-q1&nbspisat (0,0) and&nbsp+q2&nbspat&nbsp(-4, 0).&nbsp The force of&nbsp&nbsp+q2&nbspon&nbsp-q1&nbsp&nbsppoints(a) South.&nbsp ( b) East.&nbsp (c) West.

Charge&nbsp+q1&nbspisat&nbsp(-3,0)&nbspand&nbsp-q2&nbspat&nbsp(0,3).&nbsp The force of&nbsp&nbsp+q1&nbspon&nbsp-q2&nbsp&nbsppoints(a) Southwest.&nbsp ( b) Northeast.&nbsp (c) North.

Charge&nbsp+q1&nbspisat&nbsp(-3,0)&nbspand&nbsp-q2&nbspat&nbsp(0,3).&nbsp The force of&nbsp&nbsp-q2&nbspon&nbsp+q1&nbsp&nbsppoints(a) Southwest.&nbsp ( b) Northeast.&nbsp (c) South.

PartII b. Charging rod with charge # = 100

Firstcharge the ball using the charging rod, this will be done with thecharge # = 100 and eventually make a transfer of some of the chargeto the balls. In the box it will indicate: “ball mass at = 0.050grams Charge # = 100 Charge of each ball = 4.692e-9 C”. At thispoint just Drag one ball pendulum and let it over an identicalattachment which will be above the plates. Adjust the protractor soas to find the deflection angle and start increasing the voltage.

Maximumcharge # = 120, Pith ball mass mb = 0.050 (grams), Charge on eachball = 6.168e-9 C, Rotation of the knob = 270 degrees, Minimum charge# = 100, Deflection angle = 8˚

Wbythe field&nbsp=Fs cos 0º

&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp=(qE)s

&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp=(2 x 10-9&nbspC)(200N/C)(0.02 m)

&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp=8 x 10-9&nbspJ

&nbsp

Wbythe field&nbsp=Fs cos 0º

&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp=− ΔEPE

&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp=− q(Vfinal&nbsp-Vinitial)

&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp=− (2 x 10–9&nbspC)(-4J/C)

&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp=&nbsp+8.0 x 10-9&nbspJ&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp

Results

E= F / q0 F = k |q·q0| /r2 E = k |q| / r2

Thefield has a (1/r2)

ΔPE= PEf–PEi= – Ws

V= W / q0

Theunit of potential is defined to be volt, 1V=1 J/C(jouleper coulomb).

E=ΔV/Δr± 1 nC

Charge# = 100 charge on each ball = 4.692e-9 C.

1/r

Potential difference

2

1.5

1

3.0

0.66667

4.5

0.5

7.0

0.4

10.0

Maximumvalue of E is given by,

E= k |q| / r2Taking r = 2.5m And k=8.99×109N·m2/C2.

Andq = 120CE = (8.99×109x120)/(2.52)

=1.72608 x 1011N/C

Thevalue of Force is given by the formula

F= k |q·q0| /r2

F = (8.99×109x120 x100)/(2.52)

=1.72608 x 1013

ΔPE= PEf– PEi= – Ws

ΔPE= 10.0 – 1.5

=8.5 V

ThusW = -8.5 J

V= W / q0

V= 8.5/120

=0.0708333 J/C

E=ΔV/Δr

E=(3.0 – 1.5)/ (1 – 0.5)

= 1.5/0.5

=3

Discussionand analysis

Principleof superposition is the law that the resultant of tantamount vectorsizes at a point is a component of the total of the individualextents, particularly the law that the relocation at a point in amedium experiencing basic consonant movement is equivalent to theaggregate of the removals of every individual wave.

Fromthe hypothesis of electric field and electric potential, therelationship between the two is given by the expression as takesafter: E = – ΔV/Δr This estimation of E was effectivelyascertained from the slope of the diagram, hence, the hypothesisaccurately portray the marvels being tried.

Fromthe examination the outcomes acquired were quantitative in that theestimations of potential contrast were measured up to 10.0v.The firstdiagram drawn was a straight line showing the subjective part of thetest. At the point when the potential contrast was plotted againstthe converse of sweep, it was hard to think of a straight line chart.The main choice was to draw line of best fit, consequently thesubjective examination of the outcome. There were a few mistakesexperienced amid the examination. Wellsprings of the blundersinclude: Parallax lapse, Vibration of the contraption, Change ofenviron.

Conclusion

Allin all, the analysis was fruitful in that the goal of the trial wasaccomplished. In addition, the information of superposition wassurely known. Nonetheless, the outcome acquired was a smidgen notquite the same as the normal result.