
motor principle
A particle of mass 6.0x10^8kg and charge +7.2x10^6C is travelling west. The particle enters a magnetic field of magnitude 3.0T, where it completes onehalf of a circle before exiting the field moving east. How much time does this charge spend inside the magnetic field?
$\displaystyle B= \frac{uI}{2\pi r}$
$\displaystyle r= \frac {uI}{2\pi B}$
$\displaystyle = (4\pi x 10^7)(7.2x10^6C) / (2\pi)(3.0T)$
$\displaystyle =4.8x10^13m$
$\displaystyle v= \frac {Bqr}{m}$
$\displaystyle v= (3.0T)(1.602x10^19)(4.8x10^13m) / (6.0x10^8kg)$
$\displaystyle =3.84x10^24m/s$
$\displaystyle t= \frac {d}{v}$
$\displaystyle = \frac {4.8x10^13m}{2.7683x10^36m/s}$
$\displaystyle = 1.25x10^11$