Problem 29.42 Part A You want to determine C and n by graphing the data. Select

Question

Problem 29.42

Part A

You want to determine C and n by graphing the data. Select the appropriate variables to graph on each axis that will produce a straight-line graph with a slope and intercept that will allow you to determine these constants.

Sort all variables into the appropriate bins.

Hints

Help

Reset

Horizontal axis

ln(r)

Vertical axis

ln(V/x)

Not used

V

V/x

r

1/r

SubmitMy AnswersGive Up

Correct

Part B

Express your answer using two significant figures.

C=???

SOLVE PART B PLEASE.

Problem 29.42

It is postulated that the radial electric field of a group of charges falls off as Er=C/rn, where ris the distance from the center of the group and nis an unknown exponent. To test this hypothesis, you make a field probe consisting of two needle tips spaced x=1.00mm apart. You orient the needles so that a line between the tips points to the center of the charges, and 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 follows: Distance,
r(cm) Potential difference,
V(mV) 2.0 34.7 4.0 6.6 6.0 2.1 8.0 1.2 10.0 0.6

Part A

You want to determine C and n by graphing the data. Select the appropriate variables to graph on each axis that will produce a straight-line graph with a slope and intercept that will allow you to determine these constants.

Sort all variables into the appropriate bins.

Hints

Help

Reset

Horizontal axis

ln(r)

Vertical axis

ln(V/x)

Not used

V

V/x

r

1/r

SubmitMy AnswersGive Up

Correct

Part B

Graphing either ln(V/x) versus ln(r) or ln(r) versus ln(V/x) gives a straight line. In the graph shown above, we chose to plot ln(V/x) on the vertical axis and ln(r) on the horizontal axis. From the equation for the line of best fit given, calculate the constant C.

Express your answer using two significant figures.

C=???

SOLVE PART B PLEASE.

In (AV/Ar) 3.5 3.0 2.5 2.0 1.0 In (AVA)-2.50 In)6.23 0.5- 0.0 -0.5 In(r) -4.5-4.0-3.53.0 -2.5 2.0

Explanation / Answer

Part A

ln( V / x ) is used in Vertical axis

ln( r ) is used in Horizontal axis

for small x

V / x become Er = C / rn

Part B

Er = C / rn

and E = V / s

E = 34.7 m V / 1mm

= 34.7 V/m

r = 2 cm = 0.02 m

E = 0.002 / r2.5  

n = 2.5

and C = 0.002

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