In this problem, we'll carry out some calculations based on the scenario given.

The expression for the electric field on a point on the x-axis is:

$\overline{){\mathbf{E}}{\mathbf{=}}\frac{\mathbf{x}\mathbf{q}}{\mathbf{4}\mathbf{\pi}{\mathbf{\epsilon}}_{\mathbf{0}}\mathbf{(}{\mathbf{R}}^{\mathbf{2}}\mathbf{+}{\mathbf{x}}^{\mathbf{2}}\mathbf{)}}}$

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. 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.

(a) What is the magnitude E of the electric field at the point on the x-axis with x coordinate a/2?

(b) For what value of the ratio *R/a* of plate radius to separation between the plates does the electric field at the point *x = a/2* on the *x* axis differ by 1% from the result n/ε_{0} for infinite sheets?

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Electric Fields with Calculus concept. You can view video lessons to learn Electric Fields with Calculus. Or if you need more Electric Fields with Calculus practice, you can also practice Electric Fields with Calculus practice problems.