A charged particle of mass m having kinetic energy K passes undefle...

Question

A charged particle of mass m having kinetic energy K passes undeflected through a region with electric field E and magnetic field B acting perpendicular to each other. The mass m of the particle will be : KB2 2KB2 2KE2 KE2

Accepted Answer

For the particle to pass undeflected, the electric and magnetic forces must balance (velocity selector condition):

$$qE=qvB \Rightarrow v=\frac{E}{B}$$

Kinetic energy: $K=\dfrac12mv^2 \Rightarrow m=\dfrac{2K}{v^2}=\dfrac{2K}{(E/B)^2}=\dfrac{2KB^2}{E^2}$

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