Two charges of \(\text{+3}\) \(\text{nC}\) and \(-\text{5}\) \(\text{nC}\) are separated by a
distance of \(\text{40}\) \(\text{cm}\). What is the electrostatic force between the two
charges?
\begin{align*}
F & = \frac{kQ_{1}Q_{2}}{r^{2}} \\
& = \frac{(\text{9,0} \times \text{10}^{\text{9}})(\text{3} \times
\text{10}^{-\text{9}})(\text{5} \times \text{10}^{-\text{9}})}{(\text{40} \times
\text{10}^{-\text{2}})^{2}} \\
& = \text{8,44} \times \text{10}^{-\text{7}}\text{ N·C$^{-1}$}
\end{align*}
What is the electrostatic force between the spheres?
\begin{align*}
F & = \frac{kQ_{1}Q_{2}}{r^{2}} \\
& = \frac{(\text{9,0} \times \text{10}^{\text{9}})(\text{6} \times
\text{10}^{-\text{9}})(\text{10} \times \text{10}^{-\text{9}})}{(\text{20} \times
\text{10}^{-\text{3}})^{2}} \\
& = \text{1,35} \times \text{10}^{-\text{3}}\text{ N·C$^{-1}$} \text{ towards the other
sphere}.
\end{align*}
The two spheres are touched and then separated by a distance of \(\text{60}\) \(\text{mm}\).
What are the new charges on the spheres?
The spheres are conducting and so when they touch the charge is spread equally across the two
spheres. So the new charge on each sphere is:
\[\frac{Q_{1} + Q_{2}}{2} = \frac{6+(-10)}{2} = -\text{2}\text{ nC}\]
What is new electrostatic force between the spheres at this distance?
\begin{align*}
F & = \frac{kQ_{1}Q_{2}}{r^{2}} \\
& = \frac{(\text{9,0} \times \text{10}^{\text{9}})(\text{2} \times
\text{10}^{-\text{9}})(\text{2} \times \text{10}^{-\text{9}})}{(\text{60} \times
\text{10}^{-\text{3}})^{2}} \\
& = \text{1,00} \times \text{10}^{-\text{5}}\text{ N·C$^{-1}$} \text{ towards the other
sphere}.
\end{align*}
The electrostatic force between two charged spheres of \(\text{+3}\) \(\text{nC}\) and
\(\text{+4}\) \(\text{nC}\) respectively is \(\text{0,4}\) \(\text{N}\). What is the distance
between the spheres?
\begin{align*}
F_e &= \frac{k Q_1 Q_2}{r^2} \\
\text{0,4} &= \frac{(\text{9,0} \times \text{10}^{\text{9}})(\text{4} \times
\text{10}^{-\text{9}})(\text{3} \times \text{10}^{-\text{9}})}{(d)^2} \\
\text{0,4}d^{2} &= \text{1,07} \times \text{10}^{-\text{9}} \\
d^{2} &= \text{1,07} \times \text{10}^{-\text{7}} \\
&= \text{3,3} \times \text{10}^{-\text{4}}\text{ m}
\end{align*}
Two small identical metal spheres, on insulated stands, carry charges \(-q\) and \(+3q\)
respectively. When the centres of the spheres are separated by a distance d the one exerts an
electrostatic force of magnitude F on the other.
The spheres are now made to touch each other and are then brought
back to the same distance d apart. What will be the magnitude of
the electrostatic force which one sphere now exerts on the other?
-
\(\frac{1}{4}F\)
-
\(\frac{1}{3}F\)
-
\(\frac{1}{2}F\)
-
\(3F\)
[SC 2003/11]
\(\frac{1}{3}F\)
Three point charges of magnitude \(\text{+1}\) \(\text{C}\), \(\text{+1}\) \(\text{C}\) and
\(-\text{1}\) \(\text{C}\) respectively are placed on the three corners of an equilateral
triangle as shown.
Which vector best represents the direction of the resultant force
acting on the \(-\text{1}\) \(\text{C}\) charge as a result of the forces exerted
by the other two charges?
[SC 2003/11]
a
The electric field strength at a distance \(x\) from a point charge
is E. What is the magnitude of the electric field strength at a
distance \(2x\) away from the point charge?
-
\(\frac{1}{4}E\)
-
\(\frac{1}{2}E\)
-
\(2E\)
-
\(4E\)
[SC 2002/03 HG1]
\(2E\)
