A charged particle moves along a circular path in a uniform magnetic field of \( 0.04\,\mathrm{T} \) with a velocity of \( 2\times10^{5}\,\mathrm{m/s} \). The charge to mass ratio of the particle is \( 5\times10^{7}\,\mathrm{C/kg} \). The radius of the circular path of the charged particle is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 10 cm
In a uniform magnetic field the magnetic force on the particle provides the centripetal force for its circular path.
\( \displaystyle q v B = \frac{m v^{2}}{r} \;\Rightarrow\; r = \frac{m v}{q B} = \frac{v}{(q/m)\,B} \)
\( \displaystyle r = \frac{2\times10^{5}}{5\times10^{7} \times 0.04} = \frac{2\times10^{5}}{2\times10^{6}} = 0.1\,\mathrm{m} = 10\,\mathrm{cm} \)