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Charges and Fields Electric Field due to a Point Charge Concept: the electric field due to a point charge is given by ⃑𝑬 ⃑ = π‘²π’’πŸ 𝒖 ̂𝒓 𝒓 An electric field can be visualized on paper by drawing lines of force, which give an indication of both the size and the strength of the field. Lines of force are also called field lines. Field lines start on positive charges and end on negative charges Procedure Go to the web site https://phet.colorado.edu/en/simulation/charges-and-fields Once you are at the site β€œcharges and fields” Click β€œplay”. The simulation contain the following items A positive charge particle of 1 nC = 10-9 C A negative charge particle of 1 nC = 10-9 C A sensor that shows the value of the Electric Field at any point in space in V/m A distance measuring tape in cm. A grid that shows the direction of the electric field. I. Measurement of magnitude and direction of the Electric field due to a point charge The electric field for a point charge is given by ⃑𝑬 ⃑ = π‘²π’’πŸ 𝒖 ̂𝒓 𝒓 ——— (*) Where the constant k is given by K = 8.99 x 109 Nm2/C2 For the simulation q = 10-9 C. The magnitude of the electric field is going to be measured at different directions and different distance r from the point charge. Note that the sensor in the simulation gives the value of E in Volt/meter (V/m). It can be shown that 1 V/m= 1 N/C. Notice the scale of 1 m in the grid in the lower left corner. 𝑲𝒒 ̂𝒓 as E1, actually is an Let’s denote the value for E obtained by the equation ⃑𝑬 = π’“πŸ 𝒖 experimental value because you need to measure r. Denote the value obtained by the sensor as E2. Then calculate the % difference using the formula below Note: Percent difference is practically the same as percent error, only instead of one β€œtrue” value and one β€œexperimental” value, you compare two experimental values. The formula is: ——–( **) Procedure 1. Measure the Electric Field of the point charge in a direction of 0Β° Move the positive point charge to the center of the plane. Assume this position as the origin. Click in the boxes in the upper right side to activate the electric field direction, voltage, values, grid. Use the sensor (yellow circle) to measure the Electric field at different points along the x axis. The sensor gives the value of the electric filed in V/m Complete the table below X (m) Distance from the positive test charge E2 using the sensor V/m |π‘¬πŸ | % error from from equation (*) equation (**) in N/m 0.5 1 1.5 2.0 2.5 3.0 3.5 4.0 2. Measure the Electric Field of the point charge in a direction of 90Β° with respect to +x direction Y (m) Measured vertically from the positive charge 0.5 1 1.5 2.0 E2 using the sensor (V/m) |π‘¬πŸ | % error from from equation (*) equation (**) in N/m 3. Measure the Electric Field of the point charge in a direction of 45Β° with respect to + x direction. Use the measuring tape to verify the value of r. At 45Β°, follow the diagonal of the square grid r (m) E2 using the sensor V/m |π‘¬πŸ | from equation (*) in N/m % error from equation (**) 0.705 1.41 2.12 2.82 4. Measure the Electric Field of the point charge in a direction of 45Β° with the negative x direction Use the measuring tape to verify the value of r. At 45Β°, follow the diagonal of the square grid r (m) 0.705 1.41 2.12 2.82 E2 using the sensor V/m |π‘¬πŸ | from equation (*) in N/m % error from equation (**) Analysis Do Excel plots Plot E2 vs distance x. You have to make two plots, one for the results of part 1 and one for part 2. The plots must be a scatter plot. Do not joint the points with a curve. Below is an example of the Excel plot E from the sensor (N/m) vs x (m). Data of part 1 45 40 35 30 25 20 15 10 5 0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 Questions 1. Do you obtain the same values for the electric field at directions of 0Β° and 90Β° for the same distance? 2. Do you obtain the same value of the electric field for symmetric points at a direction of 45Β° with positive x and at a direction of 45Β° with negative x? 3. Verify that the magnitude of the electric filed must be the same at points at the same distance from the charge. From your data from part 1 and 2 complete the table below Use data from part 1 and part 2 to complete the table X (m) E2 using the sensor (V/m) from part 1 Y (m) 0.5 0.5 1 1 1.5 1.5 2.0 2.0 4. Write conclusions E2 using the sensor (V/m) From part 2 % error difference using E2 for the X and E2 for the Y direction from equation (**) II. Electric Field due to two point charges. To find the electric filed of two point charges at a given point in space, apply the principle of superposition. ⃑𝑬 ⃑ 𝒕𝒐𝒕𝒂𝒍 = βƒ‘π‘¬πŸ + βƒ‘π‘¬πŸ ; ——(***) At a given distance r; E total is given by ⃑𝑬 ⃑ 𝒕𝒐𝒕𝒂𝒍 = π‘²π’’πŸ π’“πŸ ̂𝒓 + 𝒖 π‘²π’’πŸ π’“πŸ ̂𝒓 ——–(***) 𝒖 In the simulation the numerical values of q1 equal q2 are equal, and keep in mind that q2 is negative Procedure: Locate both charges positive and negative separated a distance of 4 m. Assume the origin is located at the position of the positive charge and place the positive charge to the left of the negative charge Calculate the coulomb force for a distance of 4 m |π‘­π’„π’π’–π’π’π’Žπ’ƒ| = π‘²π’’πŸπ’’πŸ π’“πŸ = _______________ N Find the total electric field of the two point charges along the axis that connects the charges. Remember the origin is located at the positive charge, and positive x is the direction to the right of the positive charge. Denote q1, r1 for the positive charge and q2 and r2 for the negative charge Complete the table: r1 (m) 1 2 3 5 6 7 -1 -2 E1 (N/C) From equation (*) Direction of E1 +X or -X .r2 (m) E2 (N/C) From equation (*) Direction of E2 +X or -X E total from equation *** (N/C) Direction +X or -X Complete the table using the sensor .r1 (m) Etotal using the sensor in V/m Direction +X or -X Etotal from the previous table (N/C) % error difference from equation (**) 1 2 3 5 6 7 -1 -2 ———(**) Question 1. The % error difference increase, decrease or is random as function of distance r. 2. Show that 1 V/m is equal to 1 N/C. Use the concept that 1 V = 1 Joule/C 3. Conclusions. Series and Parallel circuits Lab Name: Series circuit + – Parallel + – Arrange bulbs in series and parallel circuits. Include pictures of each set-up. In which set-up are the bulbs brighter? Try is for both series and parallel, if one bulb is removed will the other go out? Extra credit: If you have two batteries, can the batteries be arranged in series and parallel. Which is brighter? Explain why this is.

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