Q156 / 180 · COMEDK 2025 (10 May Shift 2) · Physics
What is the dimensional formula for electric flux?
- Correct answerA$\left[\mathrm{M}^1 \mathrm{~L}^3 \mathrm{~T}^{-3} \mathrm{~A}^{-1}\right]$
- B$\left[\mathrm{M}^1 \mathrm{~L}^2 \mathrm{~T}^{-3} \mathrm{~A}^{-1}\right]$
- C$\left[\mathrm{M}^2 \mathrm{~L}^3 \mathrm{~T}^{-3} \mathrm{~A}^{-1}\right]$
- D$\left[\mathrm{M}^1 \mathrm{~L}^3 \mathrm{~T}^{-2} \mathrm{~A}^{-1}\right]$
Solution
Electric flux $\phi_E$ is defined as the product of electric field $E$ and area $A$, given by $\phi_E = E \cdot A$.
The electric field $E$ is defined as force per unit charge, $E = \dfrac{F}{q}$. The dimensional formula for force $F$ is $[M^1 L^1 T^{-2}]$ and for charge $q$ is $[A^1 T^1]$.
Thus, the dimensional formula for electric field $E$ is $\dfrac{[M^1 L^1 T^{-2}]}{[A^1 T^1]} = [M^1 L^1 T^{-3} A^{-1}]$.
The dimensional formula for area $A$ is $[L^2]$.
Therefore, the dimensional formula for electric flux $\phi_E$ is $[M^1 L^1 T^{-3} A^{-1}] \times [L^2] = [M^1 L^3 T^{-3} A^{-1}]$.
Answer: $\left[\mathrm{M}^1 \mathrm{~L}^3 \mathrm{~T}^{-3} \mathrm{~A}^{-1}\right]$
The electric field $E$ is defined as force per unit charge, $E = \dfrac{F}{q}$. The dimensional formula for force $F$ is $[M^1 L^1 T^{-2}]$ and for charge $q$ is $[A^1 T^1]$.
Thus, the dimensional formula for electric field $E$ is $\dfrac{[M^1 L^1 T^{-2}]}{[A^1 T^1]} = [M^1 L^1 T^{-3} A^{-1}]$.
The dimensional formula for area $A$ is $[L^2]$.
Therefore, the dimensional formula for electric flux $\phi_E$ is $[M^1 L^1 T^{-3} A^{-1}] \times [L^2] = [M^1 L^3 T^{-3} A^{-1}]$.
Answer: $\left[\mathrm{M}^1 \mathrm{~L}^3 \mathrm{~T}^{-3} \mathrm{~A}^{-1}\right]$
Hence, the correct answer is option: 'A'.