Prove that a charge that enters a magnetic field with no other force takes a sprial path
If you are sure you know the proof .. nothing to worry. If you dont make sure you derive it.
Pls give every step
The importance of this proof can stun you in the exam hall.
(This might come as a bit of a let down to many of you who are used to solving very tough Question of the days. But this I feel is very important for a lot of those who dont focus on the basics)
1we will just take two velocities
one perpendicular to the magnetic field
and one along it
the one along it will not change its direction as well magnitude
but the one perpendicular to it will make a circular path (i mean to say that velocity )
if we look from the rear view the path will be a circle
so at any point of time x distance= vxt
y distance =∫vpsinθdt
but dθ/dt=w =constant (as velocity perpendicular is constant)
so y distance 0∫tvpsinwtdt = (v/w)(1-coswt)
and z distance = 0∫tvpcoswtdt
=(vp/w)sinwt
62Where are the force equations!! how did u reach some of the conclusions you did.??
This is a veyr easy question.. i am not going to accept any loopholes in this one [6]
1see the velocity along the field will not change its magnitude as well as direction as
the force =qv*B= qvBsinθ = 0 (as theta = 0)
and the velocity perpendicular to the magnetic field will have a froce always towards its centre
(the old case of cyclotron)
and this magnitude will be constant as B doesnt do any work on the system!!
62Well.. I know what you are trying to say.. And I know that you might label me crazy stupid after reading this ..
But i want a more mathematical proof
step 1 implies step 2 and so on...
I can take the argument you gave for constant speed in the x axis..
but give me a correct soln like
F=qv×B
Now F=Ma..
then you get a in terms of v
Then how do you proceed mathematically to derive what you did!
Why is v perpendicular to B? The body did not enter in a perpendicular direction! :O
sorry for being such a prick ;) But I want to see all the dirty work here!
1here only w is needed
and v is vy(v perpendicular) in this case
for w
mv2/r=qvB
so v/r=qvB/mv = w
for the mathematical derivation
we see that ifthe body has rotated to an angle θ from vertical
then its velocity makes an angle of 90- θ with the vertical
so dy/dt=vpsinθ and the result follows
similary for z
plz report if some loopholes are still left
i will be covering all of them
9simple cbseguide book thm
and yes its not always spiral
its circular also
but i know ull argue that circle is extreme case of spiral
but if u take that arguement
a circle becums ellipse,spiral
line becomes ellipse.parabola,hyperbola even spiral
:))
62Yeah that is what...
THe reason why i gave such a simple question today is not bcos you know the theorem.. but because you should know the proof fo the theorem!!
I know it very well that everyone does. But this question is a bit more basic for the less intelligent ones than you [6] [3]