Question

If the charge to mass ratio of an electron is 'A' C/kg, then the gyromagnetic ratio of an orbital electron in C/kg is

• A. $\frac{A}{4}$
• B. $A$
• C. $2A$
• D. $\frac{A}{2}$

Hint:

The gyromagnetic ratio of an orbital electron is fundamentally always exactly half of its specific charge value ($\frac{e}{2m}$). Remembering this relationship helps you avoid deriving the orbital magnetic dipole moment mechanics during an exam!

Answer 1

The Correct Option is D

Step 1: Note the given quantity.
The specific charge of the electron is $\frac{e}{m_e}=A$.

Step 2: Recall the gyromagnetic ratio.
For an orbiting electron, the ratio of its magnetic moment to its angular momentum works out to a fixed value, $\frac{e}{2m_e}$.

Step 3: Write it using $A$.
\[ \frac{e}{2m_e}=\frac{1}{2}\cdot\frac{e}{m_e}=\frac{A}{2} \]
\[ \boxed{\frac{A}{2}} \]