First slide

Magnetic field due to a moving charge

Question

Magnetic field at the centre of hydrogen like atom due to motion of electron in the $n^{th}$ orbit is proportional to

Easy

A

$\frac{Z^{2}}{n^{2}}$
B

$\frac{Z^{3}}{n^{2}}$
C

$\frac{Z^{3}}{n^{5}}$
D

$\frac{Z^{2}}{n^{4}}$

Solution

$\begin{array}{l} B = \frac{μ_{o} i}{2 r} = \frac{μ_{o} e}{T 2 r} = \frac{μ_{o} ev}{2 πrr} \\ So, B \propto \frac{v}{r^{2}} r \propto \frac{n^{2}}{Z} \\ B \propto \frac{{ZZ}^{2}}{{nn}^{4}} v \propto \frac{Z}{n} \\ B \propto \frac{Z^{3}}{n^{5}} \end{array}$

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