Question

Two balls of identical mass of 0.502 kg and with identical charges placed on them hang from the ceiling on identical strings of lengths 0.710 m as shown. If the angle with respect to the vertical that the strings form is 29.0 degrees, what is the charge on each ball? Please give your answer in micro-coulomb (i.e. do not enter a unit, but calculate your answer in micro-coulomb).

Answer 1

During equilibrium, equating forces in vertical direction:

T*cos(θ) = mg ---- (1)

where T = tension in the string

Similarly, equating forces in the horizontal direction:

T*sin(θ) = E*q = (k*q/d^2)*q = k*q^2/d^2 (electrostatic force)

Also, d/2 = L*sin(θ)

So, d = 2Lsin(θ)

So, dividing equation 1 from equation 2:

tan(θ) = Eq/mg = ( kq^2/(2L*sinθ)^2) / (mg)

=> tan (29 deg)= (9*10^9*q^2/(2*0.71*sin(29 deg))^2) / (0.502*9.8)

So, q = 1.1983*10^-5 C = 11.983 uC

Answer = 11.983