# Two sides of the same sphere

There exists a uniformly charged, thin solid hemispherical shell of radius $$R$$ and constant thickness $$t$$ with surface charge density $$\sigma$$. If the force experienced by one hemisphere of this shell due to the electrostatic field of the other can be expressed as:

$\frac { \pi k }{ { \varepsilon }_{ 0 } } \times { 10 }^{ p }$

Find the remainder when $$k+p$$ is divided by $$10$$.

Details and Assumptions:

1. $${ \varepsilon }_{ 0 }$$ is the permittivity of free space.

2. Assume $$t<<R$$.

3. $$t=2 mm$$

4. $$R=6 m$$

5. $$\sigma = 7 Cm^{-2}$$

6. $$k$$ is a natural number while $$p$$ is an integer. $$k$$ is not divisible by $$10$$.

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