Question

What is the dimensional formula for electric flux?

• A. \( [M^1L^3T^{-2}A^{-1}] \)
• B. \( [M^2L^3T^{-3}A^{-1}] \)
• C. \( [M^1L^2T^{-3}A^{-1}] \)
• D. \( [M^1L^3T^{-3}A^{-1}] \)

Hint:

Electric flux is electric field multiplied by area, so its dimensions are obtained by multiplying dimensions of \( E \) and \( L^2 \).

Answer 1

The Correct Option is D

Step 1: Write formula of electric flux.
Electric flux is given by:
\[ \phi_E = EA \]

Step 2: Write dimension of area.
\[ [A] = [L^2] \]

Step 3: Write electric field formula.
\[ E = \frac{F}{q} \]

Step 4: Write dimension of force.
\[ [F] = [MLT^{-2}] \]

Step 5: Write dimension of charge.
\[ [q] = [AT] \]

Step 6: Find dimension of electric field.
\[ [E] = \frac{[MLT^{-2}]}{[AT]} \]
\[ [E] = [MLT^{-3}A^{-1}] \]

Step 7: Find dimension of electric flux.
\[ [\phi_E] = [E][A] \]
\[ [\phi_E] = [MLT^{-3}A^{-1}] [L^2] \]
\[ [\phi_E] = [ML^3T^{-3}A^{-1}] \]