Motion ,yeah ,motion is what fascinated humankind to study physics at first.Motion of particles of micro dimensions needs special treatment which is a bit different from our study of particles of macro dimensions.

Sir,but I remember you told us that laws of physics are universal in nature .then how come the study differs according to size of object under consideration.

Yes Sir Newton laws must hold good for everything , right??

Excellent ! both of you have made valid points but the fact is that Newtonian Laws are approximations which work very well when applied to particles with macro order size and with velocities much less than that of light.Rohina ,Einstein's theory of relativity is considered much more fundamental and yields accurate precise results in every case ,one and all.

Sir,I got it.Please tell us more about the theory of relativity.

Its good to see your interest in this wonderful theory ,but let us keep it for some other day.Now we will study the motion of electrons under magnetic fields under the assumption that relativistic effects are too small and can be ignored.

Does that mean we assume that the velocity of electrons is much less than light waves

Yes .consider a orthogonal coordinate system.Lets say we have magnetic field of strength B .Without loss of generality ,we can have our Z axis pointing in the same direction as B.Now an electron with initial velocity v = v1 i+ v2 j+v3 k starts experiencing the field at time t = 0. can any of you predict the motion.

hmm...mm I think ..the motion would be complex.

No!!.Nothing in physics is complex.you'll realise this in a minute.OK as a hint consider the case when v3 = 0.can you visualize that in this case the magnetic field is perpendicular to the plane which contains the velocity vector.Now ,i think Rohina can help us .

Yes Sir,i think i have it.By the formula F = charge *(velocity vector(cross pdt)magnetic field).I see that force would be perpendicular to velocity vector and also lie in the x-y plane because it is perpendicular to magnetic field as well .i guess the motion would be circular ann..

Excellent ,I owe you a chocolate Rohina .The motion would be circular with centripetal acceleration being provided by magnetic force.Buck up Rahul,its now your turn to answer the case when v3 is not equal to zero.

No doubt Sir ,i have the answer this time .with v3 = 0 we have a circular motion.humm..right with another component of velocity there wouldn't be any extra force.that is the force would still remain the same .So motion would still be circular.

Ooo.It is circular but its centre is not fixed.component v3 causes it to move continously in the Z direction.We call this sort of trajectory as "helix".

Sir ,i am not sure if i got it.Why should the force remain same irrespective of component v3.

No problem,Rohina.Its bit different hence seems strange at first.Lets go mathematically and take the cross pdt(*) of velocity and magnetic field which we will use in formula to calculate force.((v1 i + v2 j + v3 k)(*)( B k)) = B(v2 i - v1 j) .Can you feel that the force is independent of v3 ,that is Z component of velocity.To generalise the component of velocity parallel to the magnetic field does not contribute to force .

Can we see the practical demonstration of this exciting phenomena.

Sure .Well just click on change to make parrallel component nonzero.Reclicking would make it zero.Click start and stop to start and stop motion.