A thin non-conducting rod of length $50 \,cm$ has a positive charge of uniform linear density $10^{-12} \,C / m$. Find the electric potential due to the rod at a point, which is at a perpendicular distance of $1.0 \,cm$ from one-end of the rod $\left(\varepsilon_{0}=8.8 \times 10^{-12} F / m \right)$.
- 0.02 V
- 0.04 V
- 0.06 V
- 1.02 V
The Correct Option is B
Solution and Explanation
$l=50\, cm$,
$r=1 \times 10^{-2} \,m$
and $\varepsilon_{0}=8.8 \times 10^{-12} \,F / m$
We know that, $\lambda=\frac{Q}{l}$
$10^{-12}=\frac{Q}{50\, cm }$
or $10^{-12}=\frac{2 Q}{2 \times 50\,cm }$
$10^{-12}=\frac{2 Q}{100\, cm }, $
$10^{-12}=\frac{2 Q}{1 \,m}$,
$Q=\frac{1}{2} \times 10^{-12} \,C$,
Electric potential $V=\frac{1}{4 \pi \varepsilon_{0}} \cdot \frac{Q}{r}$
$=\frac{1}{4 \times 3.14 \times 8.8 \times 10^{-12}} \cdot \frac{\frac{1}{2} \times 10^{-12}}{1 \times 10^{-2}}$
$=\frac{100}{221.05}=0.4 \,V$
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Concepts Used:
Electrostatic Potential and Capacitance
Electrostatic Potential
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”.
Read More: Electrostatic Potential and Capacitance
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.