- #1

Aurelius120

- 196

- 20

- Homework Statement
- Two non conducting hemispherical surfaces of uniform charge density ##\sigma## are placed on horizontal surface. Find maximum compression in each spring if both surfaces are touching each other initially

- Relevant Equations
- Force on charge in an electric field=##qE##

Spring Force=##kx##

So I know I have to equate force on a hemispherical shell with spring force to get value of compression but I can't find the force on the hemispheres

Some places that do have the solution use the formula :

$$\text{Field of non-conducting hemispherical shell= } \frac{\sigma}{2\epsilon_○} $$

This is also the formula for infinite sheet.

Then the net charge on other sphere is ##\sigma \pi r^2##

Then Option-C is correct answer

However I have two problems:

**1. I couldn't derive the formula despite trying. It also doesn't makes sense that the field is uniform. The shell is made up of rings and rings have non-uniform fields. How do I understand and derive this?**

2. The net charge on other hemisphere should be ##\sigma×2\pi r^2## Or ##\sigma×3\pi r^2##?

2. The net charge on other hemisphere should be ##\sigma×2\pi r^2## Or ##\sigma×3\pi r^2##?