Erase all the cavities!

Electricity and Magnetism Level 4

Inside a ball charged uniformly with volume density \(\rho =4 \text{ C/m}^{ 3 }\) of radius, \(R=1 \text{ m}\), there are 5 spherical cavities of radii \(r=10 \text{ cm}\). The center of each cavity is displaced with respect to the center by a distance \(a=50 \text{ cm}\). Find the sum of magnitudes of electric field strengths inside the cavities, assuming permittivity equal to 1.

The answer is of the form \(\frac { a }{ b{ \varepsilon }_{ 0 } } \)

Find: \(a+b\)

Note: There is no point of intersection between the cavities.

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