Question

Potential has the same dimensions as :

• A. Work
• B. Electric field per unit charge
• C. Work per unit charge
• D. Force per unit charge

Answer 1

The correct option is C

Work per unit charge

The explanation for the correct option:

In the case of option C,

1. Electric potential is defined as the work done needed to move the unit charge from one point to another.
2. Potential has a formula as $\mathrm{V}=\mathrm{W}/\mathrm{q}$.
3. The dimension of work is $[\mathrm{M}{\mathrm{L}}^2{\mathrm{T}}^{-2}]$.
4. The dimension of charge is $\left[\mathrm{AT}\right]$.
5. Hence the dimension of potential becomes $\left[{\mathrm{ML}}^2{\mathrm{T}}^{-3}{\mathrm{A}}^{-1}\right]$.
6. Which is the same as the dimension of work per unit charge $\mathrm{W}/\mathrm{q}$ that is $\left[{\mathrm{ML}}^2{\mathrm{T}}^{-3}{\mathrm{A}}^{-1}\right]$.

The explanation for the incorrect options:

In the case of option A,

1. Work is termed as the product of force in the direction of displacement.
2. Work has its dimensional formula as $[\mathrm{M}{\mathrm{L}}^2{\mathrm{T}}^{-2}]$.

In the case of option B,

1. Electric field per unit charge is termed as $\frac{E}{q}$.
2. It has a dimensional formula as $\left[{\mathrm{MLA}}^{-2}{\mathrm{T}}^{-4}\right]$.

In the case of option D,

1. The electric field is termed as force per unit charge.
2. It has a dimensional formula as $\left[{\mathrm{MLA}}^{-1}{\mathrm{T}}^{-3}\right]$.

Hence option C is the correct answer.