Question:

Electric potential is :

Updated On: Aug 2, 2023

scalar and dimensionless quantity
vector and dimensionless quantity
scalar and dimensional quantity
vector and dimensional quantity

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The Correct Option is C

Approach Solution - 1

It is scalar and dimensional.

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Approach Solution -2

Ans. Electric Potential is the amount of work needed to move a unit charge from a reference point to a specific point against an electric field. The reference point is Earth, although any point that falls beyond the influence of the electric field charge can be used. Electric potential difference is the external work needed to bring a charge from one location to another location in an electric field.

In the International System of Units (SI), the electric potential is expressed in units of joules per coulomb (i.e., volts), and differences in potential energy are measured with a voltmeter.

Let us use positive charge q` to calculate the potential at point A that is distanced at r from a charge q.

Now, the force exerted by the test charge q` on the charge q placed at point A will be as such,

F= k(q.q`)/r² …(1)

The electric field due to charge q at point A will be given as such, E= F/ q` (since the electric field is force per unit charge)

Placing the value of F from equation 1 we get,

E= {k(q.q`)/r²}/q`

or, E= kq/r² ….(2)

Therefore, the value of the electric potential at point A can be given as,

V= E*r …..(3)

Now, by placing the value of E from equation 2 in equation 3 we get,

V=( kq/r²)*r

thus, V= kq/r ….(4)

Let a test charge q is being moved from point R to point P against the repulsive force of charge Q.

Therefore, to bring charge q from point R to P the force required can be taken as Fext = -FE (negative because the same is a repulsive force)

Or, work done,

Or, WRP = ∫ PR F_ext. dr = -∫ PR FE. dr

The above expression explains that the work done will be stored in the form of potential energy. When the external force is thus removed, the charge q moves further from Q as a result of the repulsive force. The potential energy gets converted into kinetic energy and thus the sum remains reserved.

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Notes on electrostatic potential and capacitance

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”.

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 C_totalis 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 C_total is any one of the capacitor’s capacitance.