Question

In an electromagnetic system, a quantity defined as the ratio of electric dipole moment and magnetic dipole moment has dimensions of [M$ L^2 T^{-3} A^{-1}]$. The value of P and Q are:

• A. 1, 0
• B. 1, -1
• C. 1, 1
• D. 0, -1

Hint:

The dimensions of the ratio of electric and magnetic dipole moments can be derived from the fundamental units of charge, length, and current.

Answer 1

The Correct Option is D

The electric dipole moment is given by \( \vec{P} = q \cdot \vec{l} \), and the magnetic dipole moment is \( \vec{M} = I \cdot A \). Comparing the dimensions of the ratio \( \frac{\vec{P}}{\vec{M}} \), we have: \[ \left[ \frac{\vec{P}}{\vec{M}} \right] = \frac{[M^1 L^2 T^{-3} A^{-1}]}{[M L^2 T^{-1} A^0]} = [M^0 L^0 T^0 A^{-1}] \]
Thus, \( P = 1 \) and \( Q = -1 \). The correct answer is (4).