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a) In this experiment you are measuring the change of potential AV over small displacement Ar. In the limit Ar 0, AV/Ar would give you the derivative of V with respect to r, which is the radial component of the electric field, E, (strictly speaking, with the minus sign). Take the natural logarithm of both sides of to show that In() can be represented as a linear function of In(7), In(A) = a In(r) + b. What are the constants a and b in terms of C and n?¹ AV Ar

a) In this experiment you are measuring the change of potential AV over small displacement Ar. In the limit Ar 0, AV/Ar would give you the derivative of V with respect to r, which is the radial component of the electric field, E, (strictly speaking, with the minus sign). Take the natural logarithm of both sides of to show that In() can be represented as a linear function of In(7), In(A) = a In(r) + b. What are the constants a and b in terms of C and n?¹ AV Ar

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Hello,  I really need help with part A, part B, and Part C because I don't understand this problem can you help me with parts A, PART B, PART C, AND can you label which one is which.

Problem 3: It is postulated that the radial electric field of a group of charges falls off as E, = C/r", where Cis a constant, r is the distance from the center of the group, and n is an unknown exponent. To test this hypothesis, you make a field probe costisting of two needle tips spaced Ar= 1.0 mm apart. You orient the needles so that a line between the tips points to the center of the charges, then use a voltmeter to read the potential difference between the tips. After you take measurements at several distances from the center of the group, your data are as given in the table. Use an appropriate graph of the data to determine the constants C and n. 3 limit Ar → a) In this experiment you are measuring the change of potential AV over small displacement Ar. In the 0, AV/Ar would give you the derivative of V with respect to r, which is the radial component of the electric field, E, (strictly speaking, with the minus sign). Take the natural logarithm of both sides of Ato show that In (AV) can be represented as a linear function of In(r), In(A) = aln(r) + b. What are the constants a and b in terms of C and n?¹ b) Place the measurements In (AV) as a function of In(r) on the graph below. 2 1 7779 79 7 -3 -6 Distance, r (cm) Potential difference, AV (mV) 2.0 34.7 4.0 6.6 6.0 2.1 1.2 -7-1 S 8.0 10.0 -2 In(r) 0.6 2 AV Note that here we use A=instead of E, = -A because the minus sign is already absorbed into the potential difference values given in the table. The potential in this problem is decreasing with the distance, which means that the value of potential at the tip of the probe that is farther from the center will be smaller than the potential of the closer tip. c) If E, is indeed equal to C/r", your measurements should lic on a straight line (otherwise, you would have to conclude that the field must be described by a different function). Can you connect the dots with a straight line? Determine the constants C and n from this line (to do that, it is helpful to remember that a line y = ax + b intersects y axis at the point y = b and x axis at the point x = -b/a).
Transcribed Image Text:Problem 3: It is postulated that the radial electric field of a group of charges falls off as E, = C/r", where Cis a constant, r is the distance from the center of the group, and n is an unknown exponent. To test this hypothesis, you make a field probe costisting of two needle tips spaced Ar= 1.0 mm apart. You orient the needles so that a line between the tips points to the center of the charges, then use a voltmeter to read the potential difference between the tips. After you take measurements at several distances from the center of the group, your data are as given in the table. Use an appropriate graph of the data to determine the constants C and n. 3 limit Ar → a) In this experiment you are measuring the change of potential AV over small displacement Ar. In the 0, AV/Ar would give you the derivative of V with respect to r, which is the radial component of the electric field, E, (strictly speaking, with the minus sign). Take the natural logarithm of both sides of Ato show that In (AV) can be represented as a linear function of In(r), In(A) = aln(r) + b. What are the constants a and b in terms of C and n?¹ b) Place the measurements In (AV) as a function of In(r) on the graph below. 2 1 7779 79 7 -3 -6 Distance, r (cm) Potential difference, AV (mV) 2.0 34.7 4.0 6.6 6.0 2.1 1.2 -7-1 S 8.0 10.0 -2 In(r) 0.6 2 AV Note that here we use A=instead of E, = -A because the minus sign is already absorbed into the potential difference values given in the table. The potential in this problem is decreasing with the distance, which means that the value of potential at the tip of the probe that is farther from the center will be smaller than the potential of the closer tip. c) If E, is indeed equal to C/r", your measurements should lic on a straight line (otherwise, you would have to conclude that the field must be described by a different function). Can you connect the dots with a straight line? Determine the constants C and n from this line (to do that, it is helpful to remember that a line y = ax + b intersects y axis at the point y = b and x axis at the point x = -b/a).
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