Question

Which of the following set have different dimensions?

• A. Pressure, Young’s modulus, Stress
• B. EMF, Potential difference, Electric potential
• C. Heat, Work done, Energy
• D. Dipole moment, Electric flux, Electric field

Answer 1

The correct option is D

Dipole moment, Electric flux, Electric field

Explanation of the correct option:

Option D

Dimension:

1. The concept of dimension is that even if add or subtract the quantity remains the same.
2. The dimension formula is the expression of a physical quantity in the terms of mass, length, and time.

Dipole moment:

1. A dipole moment arises whenever a separation between the system
2. The formula of the dipole moment $\text{Electric dipole moment=charge × distance between charges}$
3. The dimension formula for $\mathrm{Electric}\mathrm{dipole}\mathrm{moment}=\left[\mathrm{AT}\right]\mathrm{x}\left[\mathrm{L}\right]=\left[\mathrm{ALT}\right]$

Electric field intensity:

1. The electric field intensity is the strength of the electric field at the point
2. It is the force experienced by the unit positive charge in that point
   $\overrightarrow{\mathrm{E}}=\frac{\overrightarrow{\mathrm{F}}}{{\mathrm{q}}_0}$
   where, $F$ represents force, and the $q_0$ is the test charge.
3. The dimension formula for Electric field intensity
   :$$\begin{gathered} E=\frac{\left[ML{T}^{-2}\right]}{\left[AT\right]} \\ E=\left[ML{T}^{-2}\right]{\left[AT\right]}^{-1} \\ E=\left[ML{T}^{-3}{A}^{-1}\right] \end{gathered}$$
   Electric flux
4. The electric flux around an area inside an electric field is the total lines of forces passing through that area.
5. The equation of the electric flux:
   $∆{\varphi }_E=E∆S$
   where $E$ is the electric field, $∆S$ is the area element.
6. The dimension formula for Electric flux
   $$\begin{gathered} {\varphi }_E=\left[ML{T}^{-3}{A}^{-1}\right]{\left[L\right]}^2 \\ {\varphi }_E=\left[ML{T}^{-3}{A}^{-1}\right] \end{gathered}$$
   

Explanation of the incorrect options:

Option A

Pressure, Young’s modulus, Stress

1. The pressure is dimensionally represented as M¹ L^-1 T ^-2.
2. Young’s modulus M L^-1 T ^-2.
3. Stress is dimensionally represented as [M¹ L^-1 T^-2].
4. The dimensional formula for Pressure, Young’s modulus, Stress are same
   

Option B

EMF, Potential difference, Electric potential

1. Electromotive Force or EMF is dimensionally represented as [M¹ L² T^-3 I^-1].
2. The Potential difference is dimensionally represented as [M¹ L² T^-3 I^-1].
3. Electric potential is dimensionally represented as [M¹ L² T^-3 I^-1]
4. The dimensional formula for EMF, Potential difference, Electric potential are same.

Option C
Heat, Work done, Energy

1. Heat , heat energy is dimensionally represented as [M¹ L² T^-2].
2. Work done is dimensionally represented as [M¹ L² T^-2].
3. Energy is dimensionally represented as M¹ L² T^-2.
4. The dimensional formula for Heat, Work done, and Energy are the same.
   Hence, Option D is the correct answer.