Problem 4

   What is the magnitude of the force that a charge of 25\(\mu\)C exerts on one of 2.5mC at a distance of 28cm.
Which is solved with the following formula:
\(F=K\frac{Q1\ Q2}{r2}\)
Data
Q1= 25\(\mu\)C
Q2= 2.5mC
r= 28cm
\(k=9x10^9\) \(\frac{Nm^2}{C^2}\)
Substituting the formula
\(\frac{9X10^9\left(25X10^{-6}\right)\left(2.5X10^{-3}\right)}{\left(0.28\right)^2}\) \(=7174N\)

Problem 5

Two charged particles exert a force of \(3.2X10^{-2}\)N between them, which is the force if it moves only one eighth of the distance that is found.
The formula for this exercise is  \(F1r1^2=\ F2\ r2^2\)
\(F1=\ 3.2X10^{-2}N\)
\(r2=\frac{r1}{r2}\ .\ ^..\ \frac{r}{r2}=8\)
\(F2=\frac{F1r1^2}{r2^2}\ =\ \left(\frac{r1}{r2}\right)^2F1\)
\(=64\left(3.2X10^{-2}N\right)\)
\(=2.04N\)

Problem 6

Two charged spheres are separated by cm, move and you find that the force between them is tripled. How far are they now?
The following formula is used knowing that
\(F1r1^2=\ F2\ r2^2\)
\(F2=3F1\)
\(r2^2=\frac{F1}{F2}r1^2\ \ =\left(\frac{1}{3}\right)r1^2\)
\(r2=\sqrt{\frac{1}{3}\ r1}\)
\(=\frac{r1}{\sqrt{3}}=\ 4.87cm\)