# Not always a sphere!

**Electricity and Magnetism**Level 5

The electric field strength depends only on the \(x\) and \(y\) coordinates according to the law \(\vec{E} = a(x\hat{i} + y\hat{j})/(x^2 + y^2)\), where \(a\) is a constant.

Find the flux of the vector \(\vec{E}\) through the closed surface \(x^4 + y^4 + z^4 = 81\).

If it can be expressed \(k\pi a\) then give the value of \(\left \lfloor{100k} \right \rfloor\).

\[\] **Notation**: \( \lfloor \cdot \rfloor \) denotes the floor function.