JEE Main 202522 JanuaryEvening Shift

Exam: JEE Main
Year: 2025
Date: 22 January
Shift: Evening Shift
Subject: Physics
Chapter: Magnetic Effects of Current

JEE Main 2025 · 22 January · Evening Shift · Physics · Magnetic Effects of Current

An electron projected perpendicular to a uniform magnetic field B...

An electron projected perpendicular to a uniform magnetic field B moves in a circle. If Bohr's quantization is applicable, then the radius of the electronic orbit in the first excited state is :

Options

A $\sqrt{\frac{\mathrm{h}}{\pi \mathrm{eB}}}$
B $\sqrt{\frac{2 h}{\pi e B}}$
C $\sqrt{\frac{h}{2 \pi e B}}$
D $\sqrt{\frac{4 \mathrm{~h}}{\pi e B}}$

Correct answer

A. $\sqrt{\frac{\mathrm{h}}{\pi \mathrm{eB}}}$

Step-by-step solution

m v r=\frac{n h}{2 \pi}

...(i)

r=\frac{v m}{B q}

....(ii)

\begin{aligned} & n=2 \\ & m r\left(\frac{r B q}{m}\right)=\frac{2 h}{2 \pi} \\ & r=\sqrt{\frac{h}{\pi B q}} \\ & q=e \\ & r=\sqrt{\frac{h}{\pi B e}}\end{aligned}

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