Need help with Problem.

  • #1
Hi everybody,
I was wondering if somebody could help me with this problem. "A thin nonconducting rod of finite length L has a charge of q spread uniformly along it. Show that E = (q / 2πεoy) (1/{ [L² + 4y²]^1/2}) gives the magnitude E of the electric field at point P on the perpendicular bisector of the rod." I got to the part where it is E = (1/ 4π εoy) (λdx / r²). Then it says, in the expression for dE, replace r with an expression involving x and y. When P is on the perpendicular bisector of the line of charge (which it is) find an expression for the adding component of dE. That will introduce either sin (theta) or cos (theta). Reduce the resulting ttwo cariables x and theta to one, x, by replacing the trigonometric function with an expression (its definition) involving x and y. Integrate over x from end to end of the line of charge. Yeah, that sounded confusing and I ended up erasing a lot. Could anybody help?
Thanks, Karen.
 

Answers and Replies

  • #2
1,789
4
Consider a point on the perpendicular bisector of this finite rod, at a distance of y units from it, so that dq = λdx and x ranges from -L/2 to +L/2. Due to symmetry, the horizontal components will cancel.

Now integrate the expression for the vertical component. You can either express the integral in terms of x which varies from -L/2 to +L/2 or theta. Try this first...
 

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