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Question: problem 1 5 pt the magnitude of the electric force...

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Problem 1: 5 pt The magnitude of the electric force betwen two particles with where & is a constant and r is the distance betwen the two particles Suppose mow that there is a thin red that extends from -0 to x-2 with total charge Q and that this charge is distribsted over the tod uniformly. Now, a particle with charge g units is placed at z Colobs law ennot be applied directly becaise the magnitudes of the forees exeeted by different segments of the rod on the partile at r-3 are different! Tas, the rod cannot be treated as a particle So, what do we do? Lets try the Slace, Appeonimate Integrate proceue Step I: Slice In graeral, we dinde the rod between -0 and2 up into n picons of unie width as. Until further specisd, we will week with n-เด็08. On the picture below: Divide the rod into 5 slices . Shade the knarth slice, and label its thidans with Δ . ·Label the distance r between the right etĺpoint of the knith segmeit and the charge q Step 2: Approximate What should we do in this step? We have a resule that allows us to compute the force F between two particles, so we should approximate each slice as a parficle 16 Figure & Make sure you label this picture Question 1: By assuming that the fourth segment in your picture above is a particle, caleulate the total Sorce it exerts on the partile . Your atower should be in terms of and g, but you should find actual numeric values for Ar and r from your picture Hent:To find the charge of the slice, note that since the charge is uniform, the charge Qs of the srgment is givee by: length of segment eth of rol(etal charge of rd)
Now, assume that we have divided the rod isto maay slices, and coasider the sall slice ofwidth Δr krated at ras shown below Ax 17 Question 2: By auming that the slice in the picture belom is a partick, calculate the total force it exerts on the particle q. Your atmer ,heald be in terms of Q, g, and Δ Miut To find the charge ol the slice, recall the thickness of the slice is Ar To find the distance r between the slice and the particle with charge g, mote that the slice located at 1 and the particle located at 1-3. In the case when Ar-1/2.980-4-1, the result should be 20k this to check if youur expesion is Question 3: Write down an integral that gives the total force, F,that the rod exerts on the particle. Your answer should be in terms of Q. gPay attestion to the limits o stegration Question 4: Evaluate the integral you wrote down in order to compute the total force the rod exerts on the particle 18
Problem 2: 5 ptsThe magnitude of the electric force that a od whone left edge is at 0 with total charge Qof uniform density and length L erts on a particle aligne with it of charge g is given by kQu rs - L) where r is the distance betwees the particle and the (farther) edge of the rod and & is a ccestant On the figure below Deaw a rod with L-2 Dran the particle with charge q when -3 Label it with Question 1: Using the given formula, write F in this case Leve your aeer in term k,Q, and g Remark: Compare what youve drawn with the picture from the peviosoem Does it look similar? Coampare what you wrote for F here with your r to the last question in the previous problem Does it look similar? Hint: They soul Now suppose there are two rods 2 units aqpart that are aligned with each other, a shown belo that can be cosoted via the gie Sorsla if the finst object is a rod and the od is a particle 19 Suppose Rod 1 has chargeQ and length L-1 and that Rod 2 has total charge Q and length 2. The total boace that Rod 1 exerts on Rod 2 cannot be Sound using the Soree equation becaae Rod 2 cannot be treated as a paaticle the magnitude of the force erted Rod 1 on diferent segments of Rod 2 is differet Question 2: Using the Slice, Apprcodnate, ntegrate peocedure, write dows a integral that represents the force that the Rod I ts on tod 2 Le your in terms of Q.Q and k int: We kno how to compute the Sonce betwen Rod 1 aand a particle, so alter we slice Rod 2. we should approximate each slice as a
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