VLab Electric Field and Potential 2020 PDF

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Virtual Lab: Electric Field and Potential Name (s): Date: After you finish, please save this document, and enter your answers in the accompanying lab quiz on eCampus for a grade. You do not need to submit a completed lab report for this lab. Objectives To explore the concepts of the electric field and electric potential. Theory Electric charges alter the space around them, creating what is called an electric field (E). This is similar to how masses alter the space around them creating a gravitational field. A charge placed in an electric field will experience an electric force. The electric field strength at any point in space is defined as the net electric (Coulomb) force per unit charge acting at that point, i.e.,  F  E= [1] q Electric field is a vector. The SI unit for electric field is newton/coulomb N/C, or (more practically) volt/meter, V/m. The direction of an electric field at any point is defined as the direction of the net electric force on a positive charge placed at that point. The electric field of a point charge (q) at a distance (r) is given by: E=

kq [2] r2

where K is the electrostatic constant (9 x 10 9 Nm2/C2). Faraday introduced the concept of lines of force to aid in visualizing the magnitude and direction of the total electric field about a charge or collection of charges. These concepts are listed below. 1. A line of force is always tangent to the direction of electric field. 2. The lines of force originate on positive charges and terminate on negative charges. 3 The density of the lines of force (i.e. the lines/cm or lines/cm2) in a region of space is used to represent the electric field strength in that region of space. 4 Lines of force will not cross over or touch one another. Electric fields can be represented by a scaled drawing, by first choosing a scale factor (proportionality factor) so that n number of lines/cm2 represent a certain value of field strength (volts/m).

(a)

(b) 1

Figure 1 Examine the figure above. The two figures represent a uniform electric field. If we let figure 1( a) represent an electric field with field strength of E, figure 1(b) would represent an electric field with field strength of 2 E. (Twice the numbers of field lines passes through the same region and are equally spaced). The electric potential (V) is the measure of the amount of electric potential energy per unit charge at a given location. It is a scalar quantity. It has the units of joules/coulomb (J/C) or volts (V) and is therefore also called voltage. The potential difference ( V) is the difference in electric potential between two points in space. For a uniform electric field, we have a simple relationship relating these two quantities: E=

∆V V 2−V 1 = ∆ x x 2− x 1

[3]

Where V1 and V2 are the electric potential values measured between two points located at x 1 and x2 measured in meters. The electric potential of a point charge (q) at a distance (r) is given by: V=

kQ [4 ] r

where K is the electrostatic constant (9 x 10 9 Nm2/C2). Lines or surfaces that have the same value of the electric potential at any point on them are called equipotential lines or equipotential surfaces. There is a change in electrical potential energy (work) when charges move in the direction of the electric field. There is no change in potential energy when charges move along an equipotential line or surface. Therefore, equipotential lines or surfaces are always perpendicular to electric field lines. This property is useful in the lab. To map out the electric field for a given charge distribution (or pattern), we can first map the equipotential lines or surfaces for this charge distribution. We then draw lines perpendicular to these equipotential lines to reveal the map of the electric field. We will explore this idea in this lab. Materials Required Computer with an Internet connection, Microsoft Excel and Word. Procedure To open the animation, please copy and paste the following link into the address bar of your web browser, or Ctrl + click on the link below: Charges and Fields Animation https://phet.colorado.edu/en/simulation/charges-and-fields 2

On the animation webpage, click on the picture of the animation to open it in your web browser. Part A Relationship between the electric field and electric potential of a point charge and distance. In this part of the lab, we will study how the electric field and electric potential of a point charge change with distance. We will use a free animation provided by the PhET initiative at the University of Colorado.

Hints for the animation:  In this animation, the brightness of the arrows indicates the strength of the electric field (E). The brighter the arrows, the stronger the electric field.  The directions of the electric filed lines are shown by the direction of arrows.  The brightness of the charges shows the strength of the electric potential (V). The brighter the glow around the charge the larger the magnitude of the electric potential at that point.  To reset the animation, click on the orange counterclockwise arrow in the lower right of the window. Steps: 1. Drag one +1 nC charge (red dot) from the bottom box of the animation to the middle of the screen. 2. Drag the yellow measuring tape onto the screen and place its starting mark (red crosshair) on top of the + sign of the point charge. The default starting distance measurement should read 20 cm. 3. We will measure the electric field, and electric potential at different distances from this point charge and enter our measurements in Table 1 below. 4. To measure the electric field, drag the yellow “Sensors” dot from the bottom box to the point of interest on the screen. In this, case place the yellow sensor at the 20 cm mark of the measuring tape. Click on “Values” in box on the top right. The magnitude of the electric field will be displayed in V/m next to the sensor. Enter this value in Table 1. 5. To measure the electric potential, click on the blue and white Voltmeter tool and drag it so that its crosshair aligns with the point of interest on the screen. In this case, drag it to the 20 cm mark on the measuring tape. Record the electric potential value displayed in the voltmeter in 3

Table 1. Click on the yellow pencil inside the voltmeter to display the equipotential lines around the point charge. All points on such a line will have the same electric potential (voltage value), and this line is known as an “Equipotential line." 6. The first row in Table 1 has been completed as an example. Repeat steps 4 and 5 above to measure E and V for the other distances in Table 1. Complete Table 1. Note: if you cannot get the exact distances listed in Table 1 on the animation, use the next closest values. The figures below explain how to make these measurements.

7. Calculate the theoretical values for E and V using the equations provided in the table, and enter these into the last two columns of Table 1. Example calculations for the first row are shown below: E=

9 −9 kq ( 9 ×10 )( 10 ) = =225 V /m ( 0.2) 2 r2

V=

−9 9 kq ( 9× 10 ) ( 10 ) = =45 V r 0.2

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Table 1

Distance r (m)

1/r (m-1)

1/r2 (m-2)

E (V/m) Measured

V (V) Measured

E = kq/r2 (V/m) V = kq/r Theory Theory

0.2

5

25

205

44

225

0.4 0.6 0.8 1.0 1.5 2.0

8. From your data in Table 1, make the following two graphs in Microsoft Excel: i) ii)

Electric field (E) on the y-axis vs. 1/r2 (1/distance2) on the x-axis.

iii)

Electric potential (V) on the y-axis vs. 1/r (1/distance) on the x-axis.

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45

iv)

Display the equation for the best fit line by clicking on the green + to the top right of the graph (Chart Elements) -> Trendline -> More Options -> Display Equation on chart. Add axes labels with the units, and a chart title. Copy-paste your graphs from Excel here:

9. If we compare the equations for E and V (see below), and the equation for a straight line (y = mx + c), we see that the slope of these lines is the quantity kq. In this case: E=

kq r2

and

V=

kq r

Theoretical value of slope: 9 9 2 slope =kq = ( 9× 10 ) (10 ) =9 N m /C

Enter your measured value for the slope from your V vs 1/r graph below:

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Measured value of slope: slope = ____ Nm2/C Calculate the percent error between the theoretical value, and your measured value for the slope using the following equation:

Percent error=

|theory −measured| theory

Percent error for slope =

×100

%

Questions: 1. Are the measured values for E and V in Table 1, approximately equal to the theoretical values? Answer: Yes 2. From the data in Table 1, we see that the electric field and distance have a ____ relationship. a) inverse b) inverse-square c) inverse-cube d) directly proportional 3. From the data in Table 1, we see that the electric potential and distance have a ____ relationship. a) inverse b) inverse-square c) inverse-cube d) directly proportional

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Part B Relationship between equipotential lines and electric field lines. In this part of the lab we will map the equipotential lines around a single point charge. We will study how the electric field is oriented relative to these equipotential lines. Steps: 1. Reset the animation to start over. 2. Drag one +1 nC charge (red dot) from the bottom box of the animation to the middle of the screen. 3. Drag the yellow measuring tape onto the screen and place its starting mark (red crosshair) on top of the + sign of the point charge. The starting distance measurement should read 20 cm. 4. Drag the voltmeter and place its crosshair at the 20 cm mark of the measuring tape. Click on the yellow pencil inside the voltmeter box to display the green equipotential line. You should now see a green circle surrounding the positive point charge. 5. Increase the distance on the measuring tape to 40 cm, and repeat step 4 for the 40-cm mark. 6. Repeat steps 4 and 5 for the distances 60 cm, 80 cm, 100 cm, 150 cm, and 200 cm. Note: if you cannot get these exact distances on the animation, use the next closest values.

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7. After you have plotted the green equipotential lines at all distances, click on “Direction only” in the box below the Electric Field box.

8. Study how the white arrows, which represent the direction of the electric field, are oriented relative to the green circles of the equipotential lines. This relationship in directions will be easier to see at points where the electric field vectors cross the equipotential lines (see sample picture below).

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Questions: 4. From part B of the lab, we see that the equipotential lines form _____ around a point charge. a) circles b) ellipses c) squares d) triangles 5. From part B of the lab, we see that the electric field for a positive point charge is ____. a) directed straight up and down b) directed straight left to right c) directed straight right to left d) directed radially outwards 6. From part B of the lab, we see that the electric field lines are oriented _____ to the equipotential lines. a) parallel b) perpendicular c) at 60 degrees d) at 30 degrees 7. From this lab we see that to map the electric field of an unknown charge distribution (or pattern), we would _____. a) first draw the charge distribution with all the charges. The map of the electric field is exactly the same shape as the charge distribution b) first measure the electric potential (since it is easier to measure) and draw the equipotential lines. Then draw lines parallel to these equipotential lines to make a visual map of the electric field c) first measure the electric potential (since it is easier to measure) and draw the equipotential lines. Then draw perpendicular lines to these equipotential lines to make a visual map of the electric field d) measure the electric field directly and then draw the electric field lines

8. From this lab, we learn that the electric field is a _____, and the electric potential is a _____. a) scalar, scalar b) vector, vector c) scalar, vector d) vector, scalar

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9. From this lab, we learn that the electric field and electric potential depend on both, the magnitude of the source charge (q), and the distance from the source charge (r). If we were to increase the magnitude of our source charge from 1 nC to 5 nC, then the magnitudes of the electric field and electric potential would be ____. (you can test this on the animation by dragging five 1 nC charges on top of each other and measuring E and V at a distance of 1 m). a) E = 0.9 V/C, and V = 0.9 V (ten times as less for both) b) E = 1.8 V/C, and V = 1.8 V (five times as less for both) c) E = 90 V/C, and V = 90 V (ten times as much for both) d) E = 45 V/C, and V = 45 V (five times as much for both) After you finish, please save this document, and enter your answers in the accompanying lab quiz on eCampus for a grade. You do not need to submit a completed lab report for this lab. Thank you.

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