- #1
Karol
- 1,380
- 22
Homework Statement
A disk of radius 10 [cm] is charged with 5E-9 [Coulon]. where on it's axis is the greatest electric field.
Homework Equations
The field on the axis of a charged disk:
##E=\frac{1}{4\pi\varepsilon_0}\frac{q\cdot \cos\alpha}{s^2}##
The Attempt at a Solution
I express [itex]\cos\alpha[/itex] in terms of the radius R and the diagonal distance s:
##\cos\alpha=\frac{\sqrt{s^2-R^2}}{s}##
I insert that into part of the equation of the field:
##\frac{\cos\alpha}{s^2}=\frac{\sqrt{s^2-R^2}}{s^3}##
The derivative of this expression is (maybe i have a mistake here):
##\left( \frac{\sqrt{s^2-R^2}}{s^3}\right)'=\frac{3R^2-2s^2}{s^4\sqrt{s^2-R^2}}##
I equal the numerator to 0 and get s=1.22R=12.2[cm]
The horizontal distance on the axis that corresponds to this diagonal is:
##\cos\alpha=\frac{1.22R}{R}\rightarrow\alpha=34.95^0##
To this angle the horizontal distance is 14.3[cm] while it should be around 8[cm]