Question

Two particles of identical mass m and charge q aresuspended bymeans of uncharged threads of identical length L whosemasses arenegligible. Due to the forces present, each particle isin a stateof equilibrium. Due to the symmetry of theconfiguration, eachthread forms the angle (data) with the verticaldirection, asdepicted in the diagram. Standard gravity actsverticallydownward.

a) Let T denote the magnitude of the tension force inthethread and F denote the magnitude of the electrostaticforceexerted on a particle. By constructing a proper free-bodydiagramfor either particle, show that

sin(θ)*T= F, cos(θ)*T = mg

b)By combining these equations, show that

(sin(θ))^2*tan(θ)= (K_e*q^2)/(4*L^2*mg)

c) Assume that (θ) << 1 (radian), so thattan(θ) ˜sin(θ). Determine an approximate value forθ when

m = 5.0 g, q = 25 nC, and L = 120 cm. Express this value ofθin degrees.

d) Furthermore, in the case for which tan(θ) ˜sin(θ), showthat

x˜ ((2*K_e*q^2*L)/(mg))^(1/3)

Determine an approximate value for x based upon thedataprovided above.

Please provide step by step solutions please....