A total charge 6.0 × 10-6 C is distributed uniformly throughout a cubical volume

Question

A total charge 6.0 × 10-6 C is distributed uniformly throughout a cubical volume whose edges are 5.0 cm long. (a) What is the charge density in the cube (in C/m3)? C/m3 (b) What is the electric flux (in N·m2/C) through a cube with 16.0 cm edges that is concentric with the charge distribution? N m2/c (c) Do the same calculation for cubes whose edges are 17.0 cm long and 4.0 cm long. 17.0 cm edge cube 4.0 cm edge cube N m2/C N m2/C = (d) what is the electric flux (in N·m2/C) through a spherical surface of radius 2.0 cm that is also concentric with the charge distribution? N m2/C

Explanation / Answer

a) charge density = q/Volume = 6e-6/0.05^3 = 0.048 C/m^3

b) flux = q/e0 = 6e-6/8.85e-12 = 677966 Nm^2/C

c) flux of large cube =  q/e0 =  677966 Nm^2/C

flux of small cube =  charge/e0 = 0.048*0.04^3/8.85e-12 = 347118 Nm^2/C

d) flux = charge/e0 = 0.048*4/3*pi*0.02^3/8.85e-12 = 181750 Nm^2/C

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