Two spherical conductors $B$ and $C$ having equal radii and carrying equal charges in them repel each other with a force $F$ when kept apart at some distance. A third spherical conductor having same radius as that of $B$ but uncharged, is brought in contact with $B$, then brought in contact with $C$ and finally removed away from both. The new force of repulsion between $B$ and $C$ is
Let the spherical conductors $B$ and $C$ have same charge as $q$. The electric force between them is
$F=\frac{1}{4 \pi \varepsilon_{0}} \frac{q^{2}}{r^{2}}$
$r$, being the distance between them.
When third uncharged conductor $A$ is brought in contact with $B$, then charge on each conductor
$q_{A}=q_{B}=\frac{q_{A}+q_{B}}{2}=\frac{0+q}{2}=\frac{q}{2}$
When this conductor $A$ is now brought in contact with $C$, then charge on each conductor
$q_{A}=q_{C}=\frac{q_{A}+q_{C}}{2}$
$=\frac{(q / 2)+q}{2}=\frac{3 q}{4}$
Hence, electric force acting between $B$ and $C$ is
$F'=\frac{1}{4 \pi \varepsilon_{0}} \frac{q_{B} q_{C}}{r^{2}}$
$=\frac{1}{4 \pi \varepsilon_{0}} \frac{(q / 2)(3 q / 4)}{r^{2}}$
$=\frac{3}{8}\left[\frac{1}{4 \pi \varepsilon_{0}} \frac{q^{2}}{r^{2}}\right]$
$=\frac{3 F}{8}$
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Top Questions on electrostatic potential and capacitance
The potential of a point is defined as the work done per unit charge that results in bringing a charge from infinity to a certain point.
Some major things that we should know about electric potential:
They are denoted by V and are a scalar quantity.
It is measured in volts.
Capacitance
The ability of a capacitor of holding the energy in form of an electric charge is defined as capacitance. Similarly, we can also say that capacitance is the storing ability of capacitors, and the unit in which they are measured is “farads”.
The capacitor is in Series and in Parallel as defined below;
In Series
Both the Capacitors C1 and C2 can easily get connected in series. When the capacitors are connected in series then the total capacitance that is Ctotal is less than any one of the capacitor’s capacitance.
In Parallel
Both Capacitor C1 and C2 are connected in parallel. When the capacitors are connected parallelly then the total capacitance that is Ctotal is any one of the capacitor’s capacitance.
