# An uncharged nonconductive hollow sphere of radius 17.0 cm surrounds a 16.0 µC charge located at the origin of a cartesian coordinate system.

An uncharged nonconductive hollow sphere of radius 17.0 cm surrounds a 16.0 µC 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 electric flux through the hole.
N·m2/C

asked Feb 10, 2012 in Physics

The formula for electric flux is:

electric flux = E*A (*where E = electric field, A = area)

Furthermore,

E = ke*Q / R^2  (where ke = 8.988*10^9 N*m^2/C^2, Q=charge, R=radius between the charge and point of interest)

A = area of circle = pi*r^2

plugging both of these equations into the formula for electric flux we get:

electric flux = ( ke*Q / R^2  ) * (pi*r^2)

Now you are given that,

Q = 16 µC = 16*10^-6 C

R = 17 cm = 17*10^-2 m

r = 1 mm = 1*10^-3 m

Now plugging these values into the formula for electri flux:

electric flux = (( 8.988*10^9 N*m^2/C^2) * (16*10^-6 C) / (17*10^-2 m)^2  ) * (pi*(1*10^-3 m)^2)

simplify and we get:

electric flux = 15.636 N·m2/C

answered Feb 16, 2012 by ~Expert~ (3,856 points)
selected Feb 16, 2012 by awesome