A uniform magnetic field B exists in a region. An electron projected perpendicular to the field goes in a circle. Assuming Bohr’s quantization rule for angular momentum, calculate (a) the smallest possible radius of the electron (b) the radius of the nth orbit and (c) the minimum possible speed of the electron.

Question

Philoid · Accepted Answer

Applying Bohr’s quantization rule

And as electron is projected perpendicular to the magnetic field it will follow

Using both the equations and q=e

(a)Smallest possible radius is when n=1

(b)Radius in nth orbit

(c)Using again and substituting the value of r from above

For minimum possible value n=1