Question

Table 1

q1=……-4…….		q2=……8…….
r (cm)	r2 (m2)	1/r2 (1/m2)	FE (N)
10	0.01	100	28.760
9	0.0081	123.45679	35.506
8	0.0064	156.25	44.938
7	0.0049	204.08163	58.694
6	0.0036	277.77778	79.889
5	0.0025	400	115.041
4	0.0016	625	179.751
3	0.0009	1111.11111	319.557
2	0.0004	2500	719.004
1	0.0001	10000

Using your data, create a scatter plot for r, r², and 1/r². Your graphs must have the axes labeled correctly and a trendline.

Paste your graphs bellow:

Finally, use your graphs to create a mathematical formula that describes the interaction between any 2 charges.

Data Analysis

If you look closely at your equation, you will see that the units on the left hand side of the equation are not the same as the units on the right hand side. Use the information from your graph to correct this.

A little help here. The mathematical statement you have created is a proportion. In our case, it should be two proportions. So, you need to find a constant of proportionality to make your equation complete. Find this constant and use it resolve the unit issue.

The constant is the Electrical constant k. Its’ value is listed in your text. Use your graphs to support or refute the following statement.

“The force experienced by 2 individual point charges is proportional to the product of those charges and inversely proportional to the distance between them squared.”

Answer 1

Scatterplots:

The equations are displayed on the charts.

For r,

Clearly, the units are not same,

F(N) = 813.7 - 380.2 * log(r) is the mathematical equation.

Or we can say that, for a unit increase in log(r) or log of distance, the force decreases by 380.2 units.

For r²,

Clearly, the units are not same,

F(N) = -937.02 - 190.1 * log(r²) is the mathematical equation.

Or we can say that, for a unit increase in log(r²) or log of squared distance, the force decreases by 190.1 units.

Comparing the r and r² with Force, the effect of decrease of Force by squared distance is half the effect by distance itself.

For 1/r²,

Here, the equation is perfect linear

Also. equation :

F(N) = -0.0001 + 0.2876*1/r²

i.e, for a unit increase in 1/r² or a unit decrease in r², the force decrease by 0.2876 units.

Please rate my answer and comment for doubt.