Question

In the followings, dimension of electric field is:

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

Hint:

Electric field = force/charge, and charge has dimension \([A T]\).

Answer 1

The Correct Option is C

Step 1: Write the defining relation for electric field.
Electric field is force per unit charge:
\[ E = \frac{F}{q} \]
Step 2: Write the dimensions of each quantity.
Force \(F\): \([M L T^{-2}]\).
Charge \(q\) = current \(\times\) time = \([A][T] = [A T]\).
Step 3: Substitute the dimensions.
\[ [E] = \frac{[M L T^{-2}]}{[A T]} = [M L T^{-2-1} A^{-1}] = [M L T^{-3} A^{-1}] \]
Step 4: Match with the options. This equals option (C).
Options (A), (B) and (D) do not reduce to \(M L T^{-3} A^{-1}\); (D) is actually the dimension of electric potential, not field.
\[\boxed{[M L T^{-3} A^{-1}]}\]