Coulomb’s Law Problem: Electrostatic Forces Between Charges

[nolife49]

Homework Statement

1. Use Coulomb's law to find the electric force (magnitude and direction) on q for (a) q = 2 micro C and (b) a = -4 micro C. (c) Use the definition of the electric field E = F/q to find the magnitude and direction of E in each case.

Relevant Equations

Coulomb’s Law

A) F1= 59.9N
F2=179.8N
F net= 119.9N

B) F1= 119.9N
F2=359.6N
F net= 239.7N

C) 6.00E7 NC
Left


Can anyone check my work?

 

[jbriggs444]

Homework Statement: 1. Use Coulomb's law to find the electric force (magnitude and direction) on q for (a) q = 2 micro C and (b) a = -4 micro C. (c) Use the definition of the electric field E = F/q to find the magnitude and direction of E in each case.
Relevant Equations: Coulomb’s Law

View attachment 361479


A) F1= 59.9N
F2=179.8N
F net= 119.9N

B) F1= 119.9N
F2=359.6N
F net= 239.7N

C) 6.00E7 NC
Left


Can anyone check my work?

Part (a) asked for magnitude and direction. You provided magnitude only. I agree with the number, but you've used too many significant figures.

Part (b) asked for magnitude and direction. You provided magnitude only. I agree with the number, but again, you've used too many significant figures.

Part (c) asked for magnitude and direction. You provided both (good job). However, the units you quoted are incorrect. The result should not be in Newton-Coulombs.

It is a bit ambiguous whether (c) asked for two results, one for each value of $q$. Since both results should be identical, that should not matter. But the question setter may be fishing to make sure you are aware of that fact.

I'd like to have seen a bit more work (the value of Coulomb's constant, the directions of the individual forces, the conversion from centimeters to meters). Teachers were always after me to show more work.

 

[nolife49]

Part (a) asked for magnitude and direction. You provided magnitude only. I agree with the number, but you've used too many significant figures.

Part (b) asked for magnitude and direction. You provided magnitude only. I agree with the number, but again, you've used too many significant figures.

Part (c) asked for magnitude and direction. You provided both (good job). However, the units you quoted are incorrect. The result should not be in Newton-Coulombs.

It is a bit ambiguous whether (c) asked for two results, one for each value of $q$. Since both results should be identical, that should not matter. But the question setter may be fishing to make sure you are aware of that fact.

I'd like to have seen a bit more work (the value of Coulomb's constant, the directions of the individual forces, the conversion from centimeters to meters). Teachers were always after me to show more work.

Thanks for the response.

I was thinking the same about the significant figures. As for more work, I could provide a picture of my work later with the formulas used, but I thought it would take me a long time to write everything down accurately on the keyboard.

Yes, part C asked for both the final Electric field magnitude. I forgot to include the second case, but it would also be 6.00E-7, but in this case, it would be directed to the right.

I am taking Physics 2 this semester, so not aware of any other units that could be used for C apart from N/C or V/m. Another question on this assignment asked to show that both of those units were identical.

 

[jbriggs444]

Yes, part C asked for both the final Electric field magnitude. I forgot to include the second case, but it would also be 6.00E-7, but in this case, it would be directed to the right.

You may wish to rethink that last assertion. (This is exactly what I suspect the question setter was fishing for).

I am taking Physics 2 this semester, so not aware of any other units that could be used for C apart from N/C or V/m. Another question on this assignment asked to show that both of those units were identical.

NC and N/C are different units.

The former is Newtons times Coulombs. The latter is Newtons divided by Coulombs.

 

[PeroK]

It's interesting that the question asks to calculate the force in each case first and then finally to calculate the electric field. I would have calculated the electric field first, which is independent of $q$, and used that to calculate the force in each case.

Also, it seems to me that it's not clear how many significant figures are appropriate. How precise are the distances, for example? A distance of $2cm$ could mean anything between $1.5cm$ and $2.5cm$. Or, it could be perhaps to the nearest millimeter? The same with the charges.

 

[PeroK]

PS I put the figures into a spreadsheet. I assumed that the figures were accurate to one decimal place in each case. I then calculated the error based on the maximum/minimum for each measurement. E.g. the measurement of $2.0cm$ would be in the range $1.95-2.05cm$. The magnitude of the electric field is then in the range $5.3-6.7 N/C$. That shows you how significant the error becomes.

I then did another calculation assuming that the measurements were accurate to two decimal places. E.g. the measurement of $2.00cm$ would be in the range $1.995-2.005cm$. In this case, the electric field is in the range $5.92-6.06 N/C$. It's only with that precision in the original measurements that we get the electric field narrowed down to $6 N/C$.

 

[kuruman]

PS I put the figures into a spreadsheet. I assumed that the figures were accurate to one decimal place in each case. I then calculated the error based on the maximum/minimum for each measurement. E.g. the measurement of $2.0cm$ would be in the range $1.95-2.05cm$. The magnitude of the electric field is then in the range $5.3-6.7 N/C$. That shows you how significant the error becomes.

I then did another calculation assuming that the measurements were accurate to two decimal places. E.g. the measurement of $2.00cm$ would be in the range $1.995-2.005cm$. In this case, the electric field is in the range $5.92-6.06 N/C$. It's only with that precision in the original measurements that we get the electric field narrowed down to $6 N/C$.

I put the numbers from the figure in my spreadsheet and did the calculation for the electric field assuming the standard convention "to the right is positive".
I formatted the answer cell to "Scientific" and "0 decimal places" to match the input data accuracy.
With q₁=3E-6, x₁=3E-2, q₂=4E-6, x₁=2E-2 and k=9e9, I got "-6.+07" in the cell. The units are N/C.

A spreadsheet is very convenient (and far better than a slide rule) for formatting answers to the appropriate accuracy and keeping track of powers of 10.