A pendulum of mass 80 mg carrying a charge of 2×10^4 vm^-1. Find the tension in the thread of the pendulum and the angle it makes with the vertical
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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