Answer the following questions:
A magnetic field that varies in magnitude from point to point but has a constant direction (east to west) is set up in a chamber. A charged particle enters the chamber and travels undeflected along a straight path with constant speed. What can you say about the initial velocity of the particle?
When a charged particle enters a magnetic field it experiences a force known as Magnetic Lorentz Force which is given by:
Where 
is the force on the Charged particle having charge q,moving with a velocity 
in a magnetic Field 
Note: 
, 
and 
are vector quantities, and charge q is a scalar quantity, and 
is the cross product or vector product of 
and 
, so resultant is perpendicular to plane containing 
and 
if we evaluate the formula we get,
Where, 
and 
are magnitude of velocity and magnetic field respectively, θ is the angle between Velocity of particle and magnetic field and ŵ is a unit vector perpendicular to plane containing 
and 
When angle between Velocity of particle and magnetic field 
is either 
or 
i.e. particle is either moving parallel or antiparallel to the field we can see force on the particle,
F = 0 N, since sinθ = 0 when θ is either 00 or 1800,
The particle came out of the magnetic field un-deflected, and with constant velocity i.e. it did not experience any force so we can say that particle was moving in same direction as that of magnetic field i.e. from East Towards West or in opposite direction from West towards East and magnitude of velocity can be any value.
The following figure depicts both the situations
