Question

What is the unit of electric flux in terms of the base units of SI?

• A. \(kg^{-1}m^3s^{-3}A^{-1}\)
• B. \(kg\,m^3s^3A^{-1}\)
• C. \(kg\,m^3s^{-3}A^{1}\)
• D. \(kg\,m^3s^{-3}A^{-1}\)

Hint:

Electric flux: \[ \Phi_E=EA \] SI unit: \[ N\,m^2C^{-1} \]

Answer 1

The Correct Option is D

Step 1: Write the formula for electric flux.
Electric flux is: \[ \Phi_E=E\times A \] where: \[ E=\text{electric field} \] and \[ A=\text{area} \]

Step 2: Write SI unit of electric field.
Electric field: \[ E=\frac{F}{q} \] Unit of force: \[ [N]=kg\,m\,s^{-2} \] Unit of charge: \[ [C]=A\,s \] Thus: \[ [E]=\frac{kg\,m\,s^{-2}}{A\,s} \] \[ [E]=kg\,m\,s^{-3}A^{-1} \]

Step 3: Multiply by area.
Area unit: \[ [m^2] \] Therefore: \[ [\Phi_E] = kg\,m\,s^{-3}A^{-1}\times m^2 \] \[ [\Phi_E] = kg\,m^3s^{-3}A^{-1} \]

Step 4: Identify the correct option.
Hence: \[ \boxed{kg\,m^3s^{-3}A^{-1}} \] Therefore, the correct answer is: \[ \boxed{\mathrm{(D)}} \]