Question

Can you help me to solve this problem?

Assume that the sphere of radius R, has a density p and is rising with terminal velocity (constant) v by a resistive means of density and viscosity nin the presence of an electric field E. The electric field is generated by a pair of plates parallel with separation *d" to which a potential difference V is applied. Considering that a force of thrust or flotation is exerted on the sphere (Archimedes principle), a resistive force (Stokes law), in addition to its weight and electric force, calculate the charge "q" of the sphere. (Hint: express the mass of the body according to the volume of the sphere and the density of the material) + + + + + + + + + + + + Frloatation qE V Latex drop Fviscosity mg Electric field

Answer 1

Forces acting on the sphere are,

i) Force due to floatation,   ( upward)

Ffloatation PairVg

ii) Electric force , (upward)

FEqE

iii) Viscous Force , ( downward)

Fviscosity 6Tn R

iv) Weight of sphere, (downward)

W = mg

Net force on the sphere is zero, as it is moving with constant terminal velocity .

Ffloatation+FE= WFviscosity

Pair VgqE mg+6TnR

Pair Vgq pVg+677Rv

$qE=6\pi \eta R v+\rho Vg-\rho_{air}Vg$

όπηυ +ρg-Ρar Vg Ε.

Charge of the sphere is

όπηυ +ρg-Ρar Vg Ε.