How to Calculate the Force Holding Two Halves of a Charged Sphere?

[arpon]

Homework Statement

A metal sphere of radius R and total charge Q is cut into two equal halves. Find the force that is
necessary to hold the two parts together.

Homework Equations

$F = \frac{1}{4\pi \epsilon _0} \cdot \frac {q_1 q_2}{r^2}$
$\oint \vec E \cdot d \vec A = \frac{q}{\epsilon _0}$

The Attempt at a Solution

Is there any other way which is easy to calculate rather than columb's law (using calculus)?

 

[Orodruin]

Have you tried computing the electromagnetic stress tensor from the field strength and integrating it over a "well chosen" surface?