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Electric Fields Equipment and Setup: Mathematica file- ElectricFields.nb Section A: Electric Fields Due to Two Charges Computer Setup for Section A 1. The first interactive panel shows electric fields due to two point charges, Qat (-1 m,0) and Q, at (1 m,0). The controls for this panel are at the top on the left 2. The top line has two checkboxes: one to Show Axes and the other to Show Field Lines. The top line also has a slider labeled Scale Factor; this rescales the electric field vector arrows relative to the drawing. Click the checkboxes and move the slider to see what happens. To undo any changes, click the Reset button on the upper right of the panel. 3. The next line has buttons with three different values of the charges. Click these to see what happens. 4. The third line selects the point where the fields are evaluated. The five buttons give preset values for the x- and y-coordinates of this point. point to any position. Try this. You can also drag the locator (crosshairs) to move the evaluation 5. At the right of the control panel, the x- and y-components of the fields are shown. The vectors E, and E, are the electric fields due to Q and Q, respectively; these are displayed with the green arrows in the picture. E is the total field, the vector sum of E, and E Data Recording for Section A 1. Select the charge configuration Q, =-2 pC and Drag the locator to move the evaluation position along the y-axis. In the space below, describe the direction of the field along the y-axis. +2 AC (called a dipole) and check Show Axes. The direction ot on the yrexis the Held is alweys the eft sade 2. Select thesecond ch ge configuration (Q--2pC and Q-+3pC), check Show Axes and select the position (0,1 m). In the space below, record E. E, and E. These electric field vectors will be calculated in a later question. E-615m1씨n)x103 Me 3. Select the third charge configuration (Q-2 pC and Q, 3 μ。) with Show Axes checked drag the locator to a position along the x-axis between the two charges. Find the position where the electric field becomes zero. Record this position in the space below. (It suffices for the components to be less than 0.5x10 N/C, which is sufficiently small compared to E, and E.) This position will be calculated in a later question. 0,0) m
ctric Fields section B: Trajectory of a Charged Particle in a Uniform Electric Field Computer Setup for Section B Page 2 of 4 1. Now scroll down to the second interactive panel. This shows the paths of various charged particles that are shot into a region of uniform electric field. The field points left-right; a positive value of E, corresponds to a field to the right. The particle is shot in the ty-direction into this field with initial speed v 2. At the top right are two buttons, a reset button and a U-shaped update button. The left of the control 3. In the middle of the control panel you can choose the value of the initial speed v, and the electric field 4· There is also a checkbox to Animate Motion. Checking this box shows controls for animation. This 5. The Exit Data is listed below the control panel. panel allows for the selection of the particle. The choices are: electron, proton, neutron, alpha particle and positron E,. Anytime you change these values, you should then click the update button at the upper right. may slow things down too much; if so, uncheck it. Data Recording for Section B Use v, = 600,000 ms and E.-15 NC for Steps 1 through 3 below. 1. Select the electron e and record the exit data. -. 5.27b . 12 ns 2. Select the positron e and record the exit data. -5.27レ y,-- 13 cm、 3. Select the proton p and record the exit data. 0003 cm, y, ,-0003 4. Experiment with different values of E., keeping = 600,000 ms, to find the value needed for the proton to land at the same position as the electron (in Step 1). Record this value of E, below. E, 21550 NC 5. Experiment with different values of vo, using E, 15 N/C, to find the value of v, needed for the proton to land at the same position as the positron (in Step 2). Record below. m/s

ctric Fields Page 3 of 4 uestions A-1. Explain why the field of the dipole is perpendicular to the y-axis, as observed in Section A, Step 1. A-2. Derive the result in Section A, Step 2 A-3. Derive the result in Section A, Step 3. Hint: For the field E to be zero the vectors E, and E, must be opposite in direction. Since both charges are negative, the fields E, and E, point toward the corresponding charges. The only points where the fields are in opposite directions are points between the two charges on the x-axis. This gives: Use this equation to find the x-coordinate of the position where the net field is zero.

c Fields Compare the paths in Section B, Steps 1 and 2. Explain the differences and similarities. Page 4 of B-2. Calculate the components of the acceleration vector a for both the electron and positron in Section B, Steps 1 and 2. Record the acceleration of each particle in component form below. Electron: a Positron: a B-3. Calculate the speed of the electron as it leaves the screen in Section B, Step 1. B-4. Why is the protons deflection in Section B, Step 3 so small? B-5. Explain the results of Section B, Steps 4 and 5.
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