Problem 3: It is postulated that the radial electric field of a group of charges falls off as E, = C/r", where C is 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. Distance, r (cm) Potential difference, AV (mV) 34.7 6.6 2.1 1.2 0.6 2.0 4.0 6.0 8.0 10.0
Problem 3: It is postulated that the radial electric field of a group of charges falls off as E, = C/r", where C is 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. Distance, r (cm) Potential difference, AV (mV) 34.7 6.6 2.1 1.2 0.6 2.0 4.0 6.0 8.0 10.0
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Hello I really need help with part A please that is all I need is help with part A
Transcribed Image Text:Problem 3: It is postulated that the radial electric
field of a group of charges falls off as Er = C/r", where
C is 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.
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
=to show that In (AV) can be represented as a linear function of In (r), In(A) = a ln(r) + b. What
AV
Ar
are the constants a and b in terms of C and n?¹
5
b) Place the measurements In (AV) as a function of In(r) on the graph below.
4
3
2
1
0
2.1
TTTTTT
-2
-3
-4
-5
-6
-7
-6
-5
Distance, r (cm) Potential difference, AV (mV)
34.7
6.6
2.1
1.2
0.6
-4
-3
2.0
4.0
6.0
8.0
10.0
-2 -1
In(r)
0
2
3
1 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.
4
c) If E, is indeed equal to C/r", your measurements should lie 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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