Question

An electron is moving with a velocity `vecv = (3 xx 10^6 m/s)hati`. It enters a region of magnetic field `vecB = (91 mT)hatk`. 

1. Calculate the magnetic force `vecF_B` acting on electron and the radius of its path.
2. Trace the path described by it.

Answer 1

`V = 3 xx 10^6 m//s hati, vecB = (91 mT)hatk = 91 xx 10^-3 Thatk`

a. `vecF = q(vecV xx vecB)`

= `-(1.6 xx 10^-19)(3 xx 10^6hati cc xx 91 xx 10^-3hatk)`

= `436.8 xx 10^-16 (hati xx hatk)`

= `-436.8 xx 10^-16N(-hatj)`

= `436.8 xx 10^-16 N  "in"  hatj` direction

Since, `r = (mv)/(qB)`

= `(9.1 xx 10^-31 xx 3 xx 10^6)/(1.6 xx 10^-19 xx 91 xx 10^-3)`

= `(27.3 xx 10^-25)/(145.6 xx 10^-22)`

= 0.188 × 10⁻³ m

b. `vecv = hati, vecB = hatk, vecF = hatj`

V, B, and Force are mutually ⊥ to each other.