Which of the following correctly represents the variation of electric potential (V) of a charged spherical conductor of radius (R) with radial distance (r) from the center?
Which of the following correctly represents the variation of electric potential (V) of a charged spherical conductor of radius (R) with radial distance (r) from the center?
Show Hint
The Correct Option is D
Solution and Explanation
For a charged spherical conductor, the variation of electric potential (V) with radial distance (r) from the center can be represented by the equation:
V = \(\frac {kQ}{r}\)
This equation indicates an inverse proportionality between the electric potential and the radial distance. As the radial distance (r) increases, the electric potential (V) decreases.
So, the correct representation of the variation of electric potential (V) of a charged spherical conductor with radial distance (r) from the center is:
V ∝ \(\frac 1r\)
This relationship represents option (D) "Electric potential (V) is inversely proportional to the radial distance (r)" from the given choices.
So, the correct option is (D).
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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.