Equipotential and Electric Field Lines

EQUIPOTENTIAL AND ELECTRIC FIELD LINES Course: Section: Student Name: Lab Partner: Date: 09/05/2020 Objective: The object of this experiment is to study the distribution of electric potential and electric field by measuring electric potential around electric charges of different configurations. Physical Principle: An electric charge will distort the space around itself. This spatial distortion is known as electric potential (V) and is proportional to the magnitude of the charge (Q). The electric potential of a small charge is inversely proportional to the distance (r) from the charge. Threfore :V =k Q ' 9 2 2 , where k is Coulom b sconstant (9.0 ×10 V .m /C ) r The electric field (E) produced by a charge can also be calculated by dividing the rate of change of electric potential (∆V) by the distance traveled by the charge (∆r). E= ∆V ∆r By placing a smaller test charge (q) in the proximity of the original charge (Q) and measuring the force (F) acting it, the electric field associated with the charge can be reviled. This allows the strength and direction of the electric field(E) to be determined by calculating the magnitude and direction of the force (F) acting on the test charge. E= F q The work required to move one unit of a positive charge between two points (e.g. point a and b) is proportional to the difference of electric potential between those points(∆Vab). Since charges may be positive or negative and like charges repel while opposite charges attract each other, an electric field created by a positive charge will be directed towards the negative charge. This flow of charges in an electric field can be visualized using electric field lines. Electric field line are curves whose tangents point in the direction of the electric field. Equipment:         Conductive paper Adhesive copper dots and strips Cork board Metal push pins White paper (8½"x14") Carbon paper Digital multimeter with probes Connecting wires with alligator clips  3-12V Variable power supply (set to 6V) Procedure: The apparatus for configuration “a” was set up by placing a sheet of carbon paper between the conductive paper “a” and a sheet of white paper. Metallic push pins were then used to attach all three sheets to a cork board. A variable power supply set to 6V was then attached to the pins and a digital multimeter probe used to mark points of equal potential for at least five different voltages, with enough points to determine the shape of the equipotential lines for each. The procedure was then repeated using conductive paper for configurations “b” and “c”. The equipotential lines for each charge distribution was then carefully constructed, along with their perpendicular electric field lines. The electric field strength for each configuration was then calculated in three separate locations. Lab Data: Please see the attached data sheets. Calculations: Configuration A E1= 0.9 V ∆V V A −V B 4.6 V −3.7 V = =42.9 V / m = = 0.021m d AB 0.021 m ∆d E 2= 1.6 V ∆V V A −V B 3.7 V −2.1V = =28.6 V / m = = ∆d 0.056 m d AB 0.056 m E3 = 0.7 V ∆V V A −V B 2.1 V −1.4 V = = =41.2 V /m = ∆d 0.017 m d AB 0.017 m E 1= 1.0 V ∆V V A −V B 4.9 V −3.9V = =62.5 V / m = = ∆d 0.016 m d AB 0.016 m E2= 3.7 V ∆V V A −V B 4.9 V −1.2 V = =58.7 V / m = = 0.063 m d AB 0.063 m ∆d E3 = 1.8 V ∆V V A −V B 3.0 V −1.2 V =56.3 V /m = = = 0.032m 0.032 m d AB ∆d E 1= 0.9V ∆V V A −V B 4.9 V −4.0 V = = = =47.4 V / m d AB 0.019 m ∆d 0.019 m Configuration B Configuration C E 2= 0.9V ∆V V A −V B 4.9V −4.0 V = =81.8 V /m = = 0.011 m ∆d 0.011 m d AB E3 = ∆V V A −V B 2.0 V −0.8V 1.2 V =60.0V /m = = = 0.02 m ∆d d AB 0.02 m Discussion: In this experiment, equipotential lines were successfully plotted by marking the positions of a given charge along the surface of a conductive paper. Connecting these points, we were able visualize a 2dimensional representation of the equipotential lines between these charges. Running perpendicularly to the equipotential lines from the positive charge to the negative charge are electric field lines. For point charges, the charge radiates from the charge in all directions and would form a spherical threedimensional shape. Also, the electrical field lines between two parallel charges were observed to be relatively uniformed in ‘configuration B’. Configuration C was found to have the same voltage of 3.2V within the small box formed by conductors. This was expected as the electric field does not penetrate inside the conductor, allowing the space inside the conductor to maintain the same voltage as the conductor itself. Errors may have occurred throughout this experiment which caused a distortion of the results which were obtained. Gross/personal errors may have occurred while plotÝng the equipotential and electrical field lines. Also, when marking the points of specific charges there might have been slight differences in voltage since only two significant figures were used when reading the voltage meter. Conclusion: The distribution of electric potential and electric field between two charges of different configurations was successfully observed. They were then plotted by measuring the distribution of electric potential around these charges and plotÝng their equipotential and electric field lines. Answers to Questions: 1. Is it possible for two different equipotential lines to cross each other? Explain why or why not? Equipotential lines can never cross because equipotential lines connect points of the same electric potential. Crossing equipotential lines would indicate that the point at which they cross has two separate electric potentials. The electric potential of a given point in space can only have a single value at a given time, therefore it is impossible for a given point to have two different charges. 2. Is it possible for two different electric field lines to cross each other? Explain why or why not? It is not possible for electric field lines to cross. An electric field line shows the region in space where one charge experiences a force in a particular direction from another. Since it is not possible for a force on a charge at a given point in space to act in two directions simultaneously, two electric field lines cannot cross. 3. Where do the electric field lines begin and end? If they are equally spaced at their beginning, are they equally spaced at the end? Along the way? Why? Electric field lines begin on positive charges and radiate away from them toward negative charges, where they terminate. Electric field lines are not equally spaced, they are closer together near the charges but further apart when they are further from the charges. This is because the electric field is stronger near to the charges but weaker at a distance, causing the electric field lines to be more spread out. 4. If you wanted to push a charge along one of the electric field lines from one conductor to the other, how does the choice of electric field line affect the amount of work required? Explain. The work required to move a charge along an electric field line depends on the magnitude of the charge and the potential difference through which the charge is being moved. Moving a charge along a uniformed electric field line would require less work since the electric field is constant the electric field line is usually shorter. Moving a charge along a less uniformed electric field line would require more energy since the lines get more widely spaced in weak electric fields. This would result in greater energy being required to move the charge over a greater distance. 5. The potential is everywhere the same on an equipotential line. Is the electric field everywhere the same on an electric field line? Explain. The electric field on an electric field line is not the same since electric fields get weaker as they move further away from the charge. However, the electric field between parallel lines is relatively constant. 6. How much work has to be done in order to move an electric charge along an equipotential line? No force is required to move an electric charge along an equipotential line because the electric potential is the same along an equipotential line and no force is required because there is no change in charge. 7. Where do the equipotential lines begin and end? Explain. Electric potential is the amount of energy stored in an electric charge due to its position in an electric field. Equipotential lines are always perpendicular to electric field lines, therefore there is no true beginning and end.