An uncharged, nonconducting, hollow sphere of

radius 10.0 cm surrounds a 10.0-uC charge located

at the origin of a Cartesian coordinate system. A drill

with a radius of 1.00 mm is aligned along the z axis,

and a hole is drilled in the sphere. Calculate the elec-

tric flux through the hole.

The whole surface of hollow sphere = 4π r²

= 4 x 3.14 x (10 x 10⁻²) ²

= 12.56 x 10⁻² m²

Area of the hole (both side) = 2 x π r²

= 2 x 3.14 x (10⁻³) ²

= 6.28 x 10⁻⁶ m²

flux coming out of given charge at the centre as per Gauss's theorem

= q / ε₀ where q is charge at the centre and ε₀ is permittivity of the medium.

= 10 x 10⁻⁶ / 8.85 x 10⁻¹²

= 1.13 x 10⁶

This flux will pass through the surface of sphere so flux passing through per unit area

= 1.13 x 10⁶ / 12.56 x 10⁻²

= 8.99 x 10⁶ weber per m²

flux through area of hole

= 8.99 x 10⁶ x 6.28 x 10⁻⁶

= 56.45 weber.