A uniform electric field 36 106 Vm was created in oil of de

A uniform electric field 3.6 × 106 V/m was created in oil of density 800 kg/m3 . A charged sphere of the radius 5 mm and the density 8600 kg/m3 is placed in this oil. Determine the charge of this sphere if it remains at rest in the oil. the answer is 1.1E-8 c but i dont know how to get there

Solution

electric field, E =  3.6 × 106 V/m

Density of oil: p = 800 kg/m3

radius: r = 5 mm

density of sphere: ps = 8600 kg/m3

the charge is calculated as follows:

force F= EQ

mg = EQ

Q = mg/E

= [p+ps][V]g/E

=  [ps-p][4/3][pi*r^3]g/E

= [8600-800][4/3][pi*0.005*0.005*0.005][9.8]/3.6 × 106

= 1.1E-8 C