Dimensional Formula of Electric Potential

The dimensional formula of electric potential is given by,

[M¹ L² T^-3 I^-1]

Where,

• M = Mass
• I = Current
• L = Length
• T = Time

Derivation

Since, Potential energy = Charge of particle × Electric potential

Therefore, electric potential =  Potential energy × [Charge of a particle]^-1 . . . . (1)

Since, electric charge = electric current × time

∴ The dimentional formula of electric charge = [I¹ T¹] . . . . . (2)

Since, Potential Energy = M × g × h . . . . . . (3)

The dimensions of height (h) and Mass (M) = [M⁰ L¹ T⁰] and [M¹ L⁰ T⁰] . . . . (4)

And, the dimensional formula of acceleation due to gravity (g) = [M⁰ L¹ T^-2] . . . . (5)

On substituting equation (4) and (5) in equation (3) we get,

Potential Energy = [M¹ L⁰ T⁰] × [M⁰ L¹ T^-2] × [M^o L¹ T⁰]

Therefore, the dimension of potential energy = [M¹ L² T^-2] . . . . (6)

On substituting equation (2) and (6) in equation (1) we get,

Electric potential =  Potential energy × [Charge of particle]^-1

Or, E_p = [M¹ L² T^-2] × [I¹ T¹]^-1 = [M¹ L² T^-3 I^-1]

Therefore, the electric potential is dimensionally represented as [M¹ L² T^-3 I^-1].

⇒ Check Other Dimensional Formulas:

• Dimensions of Light Year
• Dimensions of Dipole Moment
• Dimensions of Area
• Dimensions of Mobility
• Dimensions of Linear Density