Question

An electron moving with a velocity `vecv = (1.0 xx 10^7 m//s)hati + (0.5 xx 10^7 m//s)hatj` enters a region of uniform magnetic field `vecB = (0.5 mT)hatj`. Find the radius of the circular path described by it. While rotating; does the electron trace a linear path too? If so, calculate the linear distance covered by it during the period of one revolution.

Answer 1

Given,

`vecv = (1.0 xx 10^7 m//s)hati + (0.5 xx 10^7 m//s)hatj`

`vecB = (0.5 mT)hatj`

Since, `(mv^2)/r = qvB`

⇒ `r = (mv_x)/(qB) = ((9.10 xx 10^-31 xx 1.0 xx 10^7))/((1.6 xx 10^-19 xx 0.5 xx 10^-3))`

r = 11.3875 × 10⁻² m

r = 11.39

Now, `T = (2 pi r)/v = (2 pi m)/(qB)`

`T = (2 xx 3.14 xx 9.11 xx 10^-31)/(1.6 xx 10^-19 xx 0.5 xx 10^-3)`

T = 71.51 × 10⁻⁹ s

T = 71.51 ns

The electron traces a linear path too. For one revolution pitch,

T × v_y = 71.51 × 10⁻⁹ × 0.5 × 10⁷

= 35.75 × 10⁻² m

= 35.75 cm