In this problem, the value of charge is not mentioned. But the magnitude of electric field is given as 2*10^4 vm^-1. With all the given information we can solve the problem as below. Here I have taken the charge to be 2*10^-8 C (assumed from similar problems).
Given: mass = 80 mg = 80 × 10 -6 Kg
Charge q = 2 × 10 -8 C
E = 2 × 10 4 Vm -1
Let 'T' is tension in string and θ
is angle of string with vertical.
In equilibrium,
Tsinθ=qE ..................(1)
Tcosθ=mg ....,,,,,,,,,,,,,(2)
Divide (1) by (2), we get
tanθ=qE/mg
=> tanθ=[2*(10^−8)*2*(10^4) ]/ [80×(10^−6)×10]
=> tanθ=0.5
=> θ=27
Now Tension T = qE/sinθ = 2×(10^−8)×2×(10^4) / s in27°
T = 8.8 × 10 -4 N
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