00:01 Cycloid motion is observed when a charged particle experiences forces from both an electric field and a magnetic field. 02:12 Lorence force law and cycloid motion 04:26 Deriving equations of motion for cycloid motion. 06:53 Derivatives of sine and cosine result in their original functions with a negative coefficient. 09:09 Initial conditions and derivatives in Cycloid Motion 11:21 Calculation error detected in the given equations 14:05 Cycloid motion equations simplification 16:42 Equation for cycloid motion with moving center
See 5:30 where I introduce omega = QB/m I substitute in 6:20 to bring the equations together. Part of that is multiplying by omega since y double dot = x triple dot / omega. The first time derivative of (E/B)t is (E/B). The time derivative of that is 0. So the 2nd time derivative of (E/B)t is 0.
Super cool that you can get the cycloid with electromagnetism. There seems to be quite a few ways of getting it. I got with Snell's Law, for the most part, and I know I've seen it done with calculus of variations too.
I can understand the final x part , which has velocity E/B. But what about the Y part? Is R a constant? R = (Q*E)/(B*m) right? Then why y changes ? Well...i think the Q will rotate like the way you said, just can't explain the equation.
E is upwards en B in into the page so by that and the RHR the magnetic force is to the right Even if velocity increases and Fmagnetic increases it should still point right so i do not understand why it returns to the yaxis qualitatively
00:01 Cycloid motion is observed when a charged particle experiences forces from both an electric field and a magnetic field.
02:12 Lorence force law and cycloid motion
04:26 Deriving equations of motion for cycloid motion.
06:53 Derivatives of sine and cosine result in their original functions with a negative coefficient.
09:09 Initial conditions and derivatives in Cycloid Motion
11:21 Calculation error detected in the given equations
14:05 Cycloid motion equations simplification
16:42 Equation for cycloid motion with moving center
Shouldn't the cross product at 3:46 yield ByI - BxJ? The second term of the determinant should always get a - sign infront right?
thats what i got too
he corrected it at 5:00
See 5:30 where I introduce omega = QB/m
I substitute in 6:20 to bring the equations together. Part of that is multiplying by omega since y double dot = x triple dot / omega.
The first time derivative of (E/B)t is (E/B). The time derivative of that is 0. So the 2nd time derivative of (E/B)t is 0.
How did you make the equation for x and y in 7:25 plz reply ma
Cross product done incorrectly at 3:30
a correction needed... 2nd part of the last term will be (y-R)^2 (whole square) , not (y-R^2)
Nilima Ibrahim that's true
Super cool that you can get the cycloid with electromagnetism. There seems to be quite a few ways of getting it. I got with Snell's Law, for the most part, and I know I've seen it done with calculus of variations too.
Amazing explanation!!
At 12:43 derivative of sine is cosine and not (minus)cosine
Good catch. I think I fix it later... don't I?
jg394 Nope, I don't catch that. It ends up it doesn't matter.
yeah it doesn't matter
i was just saying :)
I can understand the final x part , which has velocity E/B.
But what about the Y part? Is R a constant?
R = (Q*E)/(B*m) right?
Then why y changes ?
Well...i think the Q will rotate like the way you said, just can't explain the equation.
thanks for your lesson !!
jg394
E is upwards en B in into the page so by that and the RHR the magnetic force is to the right
Even if velocity increases and Fmagnetic increases it should still point right so i do not understand why it returns to the yaxis qualitatively
bro ,, you did it amazing . thanks a lot
big fan of you.
So the motion is in direction perpendicular to E? I need added explanation about it :) thanks
Thanks a lot!
Beautiful
SIR =BOTH B AND E GIVE RISE TO CYCLOID MOTION --PLEASE CONFIRM
thanks
SIR - WHEN THERE IS ONLY B -THE MOTION IS CIRCLE ==WHEN WE HAVE BOTH B AND E =THE MOTION IS CYCLOID -- PLEASE CONFIRM -THANK U SIR
just saying :P