Summary of Lecture‐1 of 2nd part
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1. E, B are frame dependent. Examples: (a) Charge at rest in S, B=0 in S and not zero in S’
(b) E= E 0 in y‐direction, B= B0 in z
direction in S. Charge sent at velocity E/B in x‐direction in S, Keeps moving
with this velocity along x‐direction. In S’, it is at rest showing E=0.
2. Equations for E,B transformation stated without proof.
3. Example: Line charge λ at rest in S. E Field in S written using Coulomb’s law, B=0. Fields in S’
obtained from transformation equations. Comparing with Coulomb’s, Biot‐Savart law shows that linear charge density is
λ/√(1‐v2/c2).
Idea of length contraction introduced to get increased λ.
To get such a contraction, x’ =x‐vt modified by the factor
1/√(1‐v2/c2). y’=y, z’ = z stated.
4.Example: A point charge moving in S with velocity v. In S’ the charge is static and fields written using Coulomb’s law, B’=0. Using inverse transformation equations, E‐field obtained in S. There are questions about length contractions, and modification in coordinate transformation equations. These will be dealt in somewhat more detail, hopefully, in PHY102 under special theory of relativity. But once you take the E-B transformation equations granted, they follow naturally.
sir when we are in s' and the object let us suppose a metallic conductor then in any case can there be an electric field inside it . i am confused
ReplyDeleteWhenever you have a conductor at rest, and the charge distribution has settled, you will not have any electric field inside the material.
ReplyDeleteIn the problem at hand, if the conductor is at rest in S', there will be no net electric field inside. But if you ask for E-field due to part of the sources, it will have its contribution. When you take care of all sources, the net field is zero.
Remember S and S' are both inertial frames and in both frames, same laws of Physics work.
is the length really seen as contracted or is the phenomenon to describe increase in chargedensity only
ReplyDeletecould you please explain the idea of length contraction
ReplyDeleteSIR
ReplyDeleteIN LENGTH CONTRACTION HOW IS X' = X / [Y FACTOR]
AS [Y- FACTOR IS ALWAYS LESS THAN 1 IT WILL INCREASE THE LENGTH
sir, clearly length decreases in s' frame.
ReplyDeletenow if i take two points in x1 and x2 in s frame, seperation between them or length is x2-x1=L. now i shift to s' frame. they are now x1' and x2'. now seperation is L'= x2'-x1'=(x2-vt/√(1‐v2/c2)) - (x1-vt/√(1‐v2/c2)) =x1-x2/√(1‐v2/c2)=l/√(1‐v2/c2). here the length increases.
where am i going wrong???
1. Length contraction is real phenomena.
ReplyDelete2. If you see a length form a frame in which this length is at rest, the value of length is maximum. From any other frame, the length is moving and will be shorter.
3. S and s' are equivalent. Not that length is shorter in S' or in S. If the length is moving in a frame, it will be shorter.
4. Sumit: You have taken same t in S. If you assume that AB is at rest in S and is moving in S', you should take same t in S' and not in S. Else you assume that the length AB is at rest in S' and moving in S. Then you need not worry of time synchronization in S', as you have done. S' is then the rest frame for AB and the length here is larger.
5. x'=(x-vt)/root() is a point relation. It can be used to get length relation as Sumit has done.