Question

An electron beam enters a uniform magnetic field at a right angles to it. State the direction in which this electron beam will deflect. State the principle to determine the direction of force experienced by electron beam. What would happen if instead of electron beam, alpha particles enters the magnetic field with same velocity.

Answer 1

The electron beam will experience a force perpendicular to the plane of in which the velocity vector and the magnetic field vector lies. And the direction (side) of the force will depend on the direction of the magnetic field.

The alpha particle being positively charge will revolve in a direction opposite to the revolution of electron with a greater radius since its mass is greater.

Explanation:

The electron beam will experience a force perpendicular to the plane of in which the velocity vector and the magnetic field vector lies. And the direction (side) of the force will depend on the direction of the magnetic field.

The magnitude of the force is given by:

$F=q.(v\times B)$

$F=q.v.B\ sin\ \theta$

where

$\theta=$ angle between the velocity and the magnetic field

When alpha particle enters the same magnetic field with same velocity from the same direction then its direction of revolution will be opposite to that of electrons because of the opposite charge.

Also the radius of the revolution will greater in this case.

Which can be proven by:

$F_B=F_C$

where:

$F_B=$ force due to magnetic field

$F_C=$ centripetal force

so,

$q.v.B=m.\frac{v^2}{r}$

$r=\frac{m.v}{q.B}$

As radius is proportional to the mass.