Question

In an electromagnetic system, the quantity representing the ratio of electric flux and magnetic flux has dimension of $\mathrm{M}^{\mathrm{B}} \mathrm{L}^{\mathrm{O}} \mathrm{T}^{\mathrm{B}} \mathrm{A}^{\mathrm{S}}$, where value of 'Q' and 'R' are

• A. $(3,-5)$
• B. $(-2,2)$
• C. $(-2,1)$
• D. $(1,-1)$

Hint:

The ratio of electric flux to magnetic flux has dimensions of $LT^{-1}$.

Answer 1

The Correct Option is D

1. Electric flux ($\phi_E$) and magnetic flux ($\phi_M$) are defined as: \[ \phi_E = EA \quad \text{and} \quad \phi_M = BA \]
2. The ratio of electric flux to magnetic flux is: \[ \frac{\phi_E}{\phi_M} = \frac{E}{B} \]
3. The dimensions of $\frac{E}{B}$ are calculated as: \[ \left[ \frac{E}{B} \right] = \frac{[E]}{[B]} = \frac{MLT^{-2}A^{-1}}{MT^{-2}A^{-1}} = LT^{-1} \]
4. Consequently, the dimensions of $\frac{E}{B}$ are: \[ \left[ \frac{E}{B} \right] = LT^{-1} \]Thus, option (4) $(1,-1)$ is the correct selection.