Question

What minimum strength of magnetic field is required to balance the gravitational force on a proton moving at speed 7 ✕ 106 m/s?

Answer 1

If magnetic force on proton is balanced by its weight then we can write the equation

$F_{mag} = mg$

$qvB = mg$

now magnetic field is given by

$B = \frac{mg}{qv}$

here

$m = 1.6 * 10^{-27} kg$

$q = 1.6 * 10^{-19}C$

$v = 7 * 10^6 m/s$

$B = \frac{1.6*10^{-27}* 9.8}{1.6 * 10^{-19}*7 * 10^6}$

$B = 1.4 * 10^{-14} T$