Question

The dimensions of \( \frac{B}{E} \) are (B: Magnetic induction, E: Electric field intensity)

• A. \( M^0 L^{-2} T^1 \)
• B. \( M^0 L^{-1} T^2 \)
• C. \( M^0 L^1 T^1 \)
• D. \( M^0 L^{-1} T^{-1} \)
• E. \( M^0 L^1 T^{-1} \)

Hint:

The ratio \( \frac{B}{E} \) (magnetic induction to electric field intensity) has the dimensions \( M^0 L^{-1} T^{-1} \), which reflects the relationship between these physical quantities in electromagnetism.

Answer 1

The Correct Option is D

- Magnetic induction (B) is measured in Tesla (T), and its dimensions are \( M^1 L^0 T^{-2} A^{-1} \). - Electric field intensity (E) is measured in Volts per meter (V/m), and its dimensions are \( M^1 L^1 T^{-3} A^{-1} \). Now, calculating the dimensions of \( \frac{B}{E} \): \[ \frac{B}{E} = \frac{M^1 L^0 T^{-2} A^{-1}}{M^1 L^1 T^{-3} A^{-1}} = M^0 L^{-1} T^{1} \] Thus, the correct answer is (D) \( M^0 L^{-1} T^{-1} \).