Question

The dimensional formula of the intensity of electric field is:

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

Hint:

When deriving dimensional formulas, remember: - Electric field: \( E = \frac{F}{q} \), - Force: \( F = m a \), - Charge: \( q = I t \).

Answer 1

The Correct Option is A

The intensity of an electric field is proportional to the square of the electric field. The electric field intensity \( E \) is defined as the force experienced per unit positive charge: \[ E = \frac{F}{q}. \] Now, to find the dimensional formula of \( E \), we need to substitute the dimensional formulas of force \( F \) and charge \( q \). The dimensional formula of force is: \[ [F] = [M L T^{-2}] \] The dimensional formula of electric charge is: \[ [q] = [A T] \] Substituting these into the formula for \( E \): \[ E = \frac{[F]}{[q]} = \frac{[M L T^{-2}]}{[A T]} = [M L T^{-3} A^{-1}] \] Therefore, the dimensional formula of the intensity of the electric field is: \[ [M L T^{-3} A^{-1}] \]