Question

An electron gun G emits electrons of energy 2 ke V travelling in the positive X-direction. The electrons are requeired to hit the spot S where GS = 0.1 m, and the line GS make an angle of 60º with the x-axis as shown in figure. A uniform magnetic field Vector B parallel to GS exists in the region outside the electron gun. Find the minimum value of B needed to make the electrons hit S.

Answer 1

Kinetic energy of electron,

∴ speed of electron,

Since the velocity (Vector v) of the electron makes an angle of θ = 60º with the magnetic field Vector B, the path will be a helix. So, the particle will hit S if 

GS = nP Here n = 1, 2, 3, .........

But for B to be minimum, n = 1

Substituting the values, we have