Question

The dimensions of magnetic intensity are

• A. $[L^{1} M^{0} T^{1} I^{1}]$
• B. $[L^{1} M^{0} T^{0} I^{-1}]$
• C. $[L^{-1} M^{0} T^{0} I^{1}]$
• D. $[L^{2} M^{1} T^{0} I^{1}]$

Hint:

Magnetic intensity depends on current and inverse length, not on mass or time.

Answer 1

The Correct Option is C

Step 1: Definition of magnetic intensity.
Magnetic intensity $H$ is defined as magnetic field per unit permeability.
It can also be expressed as:
\[ H = \frac{B}{\mu} \]

Step 2: Dimensional formula of magnetic field $B$.
\[ [B] = [M T^{-2} I^{-1}] \]

Step 3: Dimensional formula of permeability $\mu$.
\[ [\mu] = [M L T^{-2} I^{-2}] \]

Step 4: Find dimensions of $H$.
\[ [H] = \frac{[B]}{[\mu]} = \frac{[M T^{-2} I^{-1}]}{[M L T^{-2} I^{-2}]} = [L^{-1} I^{1}] \]

Step 5: Conclusion.
The dimensions of magnetic intensity are $[L^{-1} M^{0} T^{0} I^{1}]$.