Register to reply 
Charged Particle Oscillating in External Constant Electric Field 
Share this thread: 
#1
Feb412, 03:02 PM

P: 5

1. The problem statement, all variables and given/known data
A mass m that has net electric charge Q is oscillating along the xdirection on one end of a spring (whose other end is anchored) of relaxed length s0. Suppose that someone then swirches on an electric field E that is uniform in space, constant in time, and which points in the +x direction. The entire system is then immersed in this electric field. a. Set up the governing differential equation of motion for the mass in a coordinate system with origin at the “anchored” end of the spring. Ignore gravity. b. Without actually deriving it, what do you anticipate that the governing differential equation in a “smart” coordinate system would be? c. Go through steps analogous to those we went through in our text discussion to show that the equivalent differential equation expressed in terms of the “right” variable is independent ofE Hint: As part of this, you will need to find the equilibrium position with the field “on.” Any idea of where to start would be greatly appreciated, thanks! 


#2
Feb412, 03:15 PM

Sci Advisor
HW Helper
Thanks
P: 26,157

hi scarletx09!
what do you you get? 


#3
Feb412, 03:46 PM

P: 5

Using F=ma I got:
Net force = Force of the electric field + Force of spring F = QE  K(xS0) = ma (xs0) = the displaced length from equilibrium that resulted in: a = (QE Kx + K(s0))/m Does that seem correct? can i set up the equation of motion from this? 


#4
Feb412, 03:53 PM

Sci Advisor
HW Helper
Thanks
P: 26,157

Charged Particle Oscillating in External Constant Electric Field
yes, the question ask for a differential equation, so use d^{2}x/dt^{2} instead of a (for part b, you may need to use the "hint") 


#5
Feb412, 04:09 PM

P: 5

Thanks so much for your guidance with part a!
From my understanding of Part B: the first equilibrium position was at s0 which led to that diff eq. and now its asking for a different (smater i guess?) diff. eq. based on a new equilibrium position with the electric field "on" I am confused about how the equilibrium position would change with the electric field on. Didn't I take it into account in Part A? 


#6
Feb412, 04:22 PM

Sci Advisor
HW Helper
Thanks
P: 26,157




#7
Feb412, 04:48 PM

P: 5

ok. the equilibrium position would occur when Fspring = Fefield
> K(xs0) = QE (xs0) = (QE)/k plugged that into my first diff. eq., the K cancelled and i got: d^2t/dt^2 = (2QE)/m 


Register to reply 
Related Discussions  
A charged particle in constant gravitational field  Classical Physics  2  
Motion of a charged particle in a constant magnetic and oscillating electric field.  Classical Physics  3  
A Charged Particle in a Uniform Electric Field  Classical Physics  3  
Force on a sphere in a constant external electric field  Introductory Physics Homework  5  
Is the electric field constant between two charged plates?  Classical Physics  4 