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: Use the potential-based definition of field.
Electric field magnitude equals potential gradient: \(E = V/d\).
Step 2: Find the dimension of potential \(V\).
Potential = work per unit charge = \(\dfrac{[M L^{2} T^{-2}]}{[A T]} = [M L^{2} T^{-3} A^{-1}]\).
Step 3: Divide by length \(d = [L]\).
\([E] = \dfrac{[M L^{2} T^{-3} A^{-1}]}{[L]} = [M L T^{-3} A^{-1}]\).
Step 4: This confirms option (C). Note option (D) is exactly the potential dimension, so it is the common trap.
\[\boxed{[M L T^{-3} A^{-1}]}\]