# Two sides of the same sphere

**Electricity and Magnetism**Level 4

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:**

\({ \varepsilon }_{ 0 }\) is the permittivity of free space.

Assume \(t<<R\).

\(t=2 mm\)

\(R=6 m\)

\(\sigma = 7 Cm^{-2}\)

\(k\) is a natural number while \(p\) is an integer. \(k\) is not divisible by \(10\).