Answer to Question #181205 in Electricity and Magnetism for Julia

Question

An alpha particle has a velocity of magnitude 500m/s and travels horizontally in space which there is an upward-directed uniform electric field of magnitude 38 N/C and a uniform magnetic field. The magnetic field makes an angle of 42⁰ with the particle's velocity vector and such causes the alpha particle to pass through the region of space undeflected.

What will be the magnitude of the magnetic field that is required to cause the alpha particle to pass through undeflected beginning with electric force and magnetic force equations?

Answer 1

$F_1=q(vBsin\alpha+E),$

$F_2=ma=\frac{mv^2}{r},$

$F_1=F_2,$ $\frac 1r=0\implies$

$vBsin\alpha+E=0,$

$B=-\frac{E}{vsin\alpha}=-0.11~T.$