Question

The dimensions of $\frac{mB}{kT}$ where $m$ is magnetic moment, $B$ is magnetic flux density, $k$ is Boltzmann constant and $T$ is temperature are ________.

• A. $ML^{-1}T^{-1}$
• B. $ML^{2}T^{-1}$
• C. $MLT^{-1}$
• D. $ML^{-2}T$
• E. $M^{0}L^{0}T^{0}$

Hint:

Ratios of similar quantities are dimensionless.

Answer 1

Answer: (E)

Step 1: Concept
$mB$ and $kT$ both represent energy.

Step 2: Meaning
Magnetic potential energy $U = -mB$. Thermal energy is proportional to $kT$.

Step 3: Analysis
Since both numerator and denominator have dimensions of energy ($ML^2T^{-2}$), the ratio is dimensionless.

Step 4: Conclusion
The dimensions are $M^0L^0T^0$. Final Answer: (E)