Brystephor
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Homework Statement
Consider two thin disks, of negligible thickness, of radius R oriented perpendicular to the x axis such that the x axis runs through the center of each disk. (Figure 1) The disk centered at x=0 has positive charge density η, and the disk centered at x=a has negative charge density −η, where the charge density is charge per unit area.
What is the magnitude E of the electric field at the point on the x axis with x coordinate a/2?
Homework Equations
We will need the equation for the electric field along the x-axis of a disk. I believe it is this:
[itex]\frac η {2∈_0} * \left( 1 - \frac x {\sqrt {(x^2+R^2)} } \right)[/itex]
I'm not sure that we will need anything else since we will be solving symbolically.
The Attempt at a Solution
We will need to find the electric fields emitted from both disks, and then add them, correct? So it seems like we should be able to just double the equation up top since the electric fields will be equivalent but in different directions, resulting in:
[itex]\frac η {∈_0} * \left( 1 - \frac x {\sqrt {(x^2+R^2)} } \right)[/itex]
However, this is incorrect. I am not sure what else to do. MasteringPhysics hint gave me a 'general form' equation of the electric field between the disks that is:
[itex]\frac η {2∈_0} * \left( 2 - \frac 1 { \sqrt {1+R^2/(x-a)^2} } - \frac 1 {\sqrt {1+R^2/x^2} } \right)[/itex]
I can see that the [itex]R^2 / x^2 = \arctanθ[/itex] but I do not understand where the [itex]\left( x - a^2 \right)[/itex] comes from or how to continue from here. Thank you.
