A charged particle moves along a circular path in a uniform magnetic field of 0.04 T with a velocity of $2 × 10^5\, m/s$. The charge to mass ratio of the particle is $5 × 10^7\, C/kg$. 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
Magnetic field $B = 0.04 \, \text{T}$
Velocity $v = 2 \times 10^5 \, \text{m/s}$
Charge to mass ratio $\frac{q}{m} = 5 \times 10^7 \, \text{C/kg}$
Radius of circular path: $r = \frac{mv}{qB} = \frac{v}{\left(\frac{q}{m}\right)B}$
$r = \frac{2 \times 10^5}{(5 \times 10^7)(0.04)}$
$r = \frac{2 \times 10^5}{2 \times 10^6} = 0.1 \, \text{m}$
Final Answer: $0.1 \, \text{m}$