Calculating Electric Force

One of the first tasks I told students in Electrostatics was to read Chapter 17 to find Coulomb’s Law for force. Go there now, and then return to this. If you don’t have the book, look up Coulomb’s Law on the internet. After you find it, keep reading below.

  1. At the midpoint, the strength of the Force due to the upper charge is:

Fu = (kq |Q| /r2) where |Q| = |Q1|, and r = a distance, r

  1. At the midpoint, the strength of the Force due to the lower charge is:

Fl = (kq |Q| /r2) where |Q| = |Q2|, and r = a distance, r

People who then begin to calculate the force that the red charge exerts on the blue charge can’t be helped on the assigned problem, because for reasons unknown to me, they are deciding not to DO the assigned problem. (But it’s a common occurrence.) The force that the red charge exerts on the blue charge has nothing to do with the assigned problem, which is to calculate the total force on a 1 C charge at the midpoint. In the above symbols, that 1 C charge would be q.

Q1 and Q2 are the red and blue charge values assigned to you. For example, for someone assigned N = 5, |Q2| = |Q1| = 5 x 10-9 C.

Two forces act on the charge q. One is caused by the red charge; one is caused by the blue charge. Both of these things are directional. Now diagram the situation to answer the following question: If the q placed at the midpoint is +1 C, will the two forces acting on it be in the same direction or opposite?

If they had been opposite, the total force would have been zero. But that’s nonsense. The two forces act in the same direction. So whatever you get for the force that is Q1 acting on q, you have to add the absolute value of that to the force you get for Q2 acting on q.

That’s the reason that mathematical ideas 1 and 2 above use charges in absolute value. Putting in a minus sign for Q1 or Q2 would mess up the entire directional argument just made and cause a total force answer of zero.

You can now look up the value of k, and then practice using the formulas above. Suppose your N is 5, and the Q1 and Q2 are 4 m apart. Calculate the total force acting on a 1 C charge placed at their midpoint:

Answer: 22.5 N r was 2 m in this problem. Many people forget to square r

And many people forget to add Fl to Fu.