A uniform magnetic field B is present in a region. An electron is projected perpendicular to the field and moves in a circle. Assuming Bohr's quantization rule for angular momentum, determine the minimum possible speed of the electron.

Step-by-step solution

When an electron moves in a circular path perpendicular to a uniform magnetic field B , the magnetic force provides the necessary centripetal force: e v B = m v^2 r r = m v e B According to Bohr's quantization rule for angular momentum: m v r = n h 2 Substituting the value of r in the above equation: m v ( m v e B ) = n h 2 m^2 v^2 e B = n h 2 v^2 = n h e B 2 m^2 v = n h e B 2 m^2 For the minimum possible speed, we take the minimum principal quantum number, n = 1 : v_ min = h e B 2 m^2