Electric field and Electric potential

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.