Question

Find the dimension of \( \frac{E}{B} \) where, E represents electric field and B represents magnetic field.

• A. \( ML^2 T^{-1} \)
• B. \( LT^{-1} \)
• C. \( L^2 T^{-1} \)
• D. \( LT^{-2} \)

Hint:

The dimension of the ratio of electric field to magnetic field is \( LT^{-1} \).

Answer 1

The Correct Option is B

The electric field \( E \) and the magnetic field \( B \) have the following dimensions: - The dimension of the electric field \( E \) is given by: \[ [E] = \frac{ML^2}{T^3 A} \] where \( A \) is the dimension of current (Ampere). - The dimension of the magnetic field \( B \) is given by: \[ [B] = \frac{ML}{T^2 A} \] Now, to find the dimension of \( \frac{E}{B} \), we divide the dimensions of \( E \) and \( B \): \[ \left[ \frac{E}{B} \right] = \frac{\frac{ML^2}{T^3 A}}{\frac{ML}{T^2 A}} = \frac{ML^2}{T^3 A} \times \frac{T^2 A}{ML} = \frac{L}{T} \] Thus, the dimension of \( \frac{E}{B} \) is \( LT^{-1} \).