The bob of a pendulum of weight 80 mg carries a charge of `2xx10^(-8)` C. The bob is at rest in a horizontal electric field of magnitude `2xx10^(4)V.m^(-1)`. Determine the tension in the string and angle of the string with the vertical. Given, `g=9.8m.s^(-2)`.

Explanation

Suppose, the string of the pendulum is inclined at an angle of `theta` with the vertical [Fig. 2.27].

Let the horizontal electric field E, tension in the string=T, charge on the bob = q. The forces acting on the bob are shown in the figure.
At equilibrium,
`Tsintheta=Eq,Tcostheta=mg`
`thereforetantheta=(Eq)/(mg)=(2xx10^(4)xx2xx10^(-8))/(80xx10^(-6)xx9.8)=25/49`
or, `theta=tan^(-1)(25/49)~~27^(@)`
Now, `costheta=cos27^(@)=0.89`
`thereforeT=(mg)/(costheta)=(80xx10^(-6)xx9.8)/(0.89)=8.8xx10^(-4)N`