Question

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

Options

• `(K B^2)/(2 E^2)`

• `(2K B^2)/E^2`

• `(2 K E^2)/B^2`

• `(K E^2)/(2 B^2)`

Answer 1

A charged particle of mass m having kinetic energy K passes undeflected through a region with electric field `vec E` and magnetic and magnetic field `vec B` acting perpendicular to each other. The mass m of the particle will be `bbunderline((2K B^2)/E^2)`.

Explanation:

Kinetic energy (K) = `1/2 mv^2`

From the condition of zero deflection:

v = `E/B`

Substitute this value of v into the kinetic energy expression:

K = `1/2 m(E/B)^2`

K = `(m E^2)/(2 B^2)`

⇒ m = `(2 K B^2)/E^2`