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Physics Question on Moving charges and magnetism

Gyromagnetic ratio is the ratio of magnetic moment (μ1)(\mu_{1}) to the orbital angular momentum (l)(l) Its numerical value for an electron is given by

A

8.8×10−12 C kg−18.8 \times 10^{-12}\,C\, kg^{-1}

B

8.8×1010 C kg−18.8 \times 10^{10}\,C\, kg^{-1}

C

1.6×10−19 C kg−11.6 \times 10^{-19}\,C\, kg^{-1}

D

6.67×1011 C kg−16.67 \times 10^{11}\,C\, kg^{-1}

Answer

8.8×1010 C kg−18.8 \times 10^{10}\,C\, kg^{-1}

Explanation

Solution

The gyromagnetic ratio is a constant. For any charged particle its value is given by μll=e2m\frac{\mu_{l}}{l}=\frac{e}{2m} For electron m=me=9.1×10−31 kgm=m_{e}=9.1 \times 10^{-31}\, kg, e=1.6×10−19 Ce=1.6 \times 10^{-19}\, C, ∴μll=1.6×10−192×9.1×10−31\therefore\frac{\mu_{l}}{l}=\frac{1.6\times10^{-19}}{2\times9.1\times10^{-31}} =8.8×1010 C kg−1=8.8\times10^{10}\,C \,kg^{-1}