Question

In a chamber, a uniform magnetic field of 6.5G (1G = 10^-4 T) is maintained. An electron is shot into the field with a speed of 4.8 x 10⁶ ms^-1 normal to the field. Explain why the path of the electron is a circle. Determine the radius of the circular orbit. (e = 1.6 x 10^-19 C, m_e = 9.1 x 10^-31 kg)
 

Answer 1

B = 6.5 x 10^-4 T, v = 4.8 x 10⁶ms^-1
Bqv = \(\frac{\mathrm{mv}^{2}}{\mathrm{r}}\)
r = \(\frac { mv }{ qB }\)
= \(\frac{9.1 \times 10^{-31} \times 4.8 \times 10^{6}}{1.6 \times 10^{-19} \times 6.5 \times 10^{-4}}\)
= 4.2 x 10^-2m
= 4.2 cm