September 17, 2017

Tension in a Pendulum inside an Electric Field

A pendulum bob of mass (80mg) carries a charge of (2*10^{-8}C) at rest in an horizontal uniform electric field of (20,000V/m ). Find the tension in the thread of the pendulum and the angle it makes with the vertical.

Discussion:

Electric force $$ F=qE=210^{-8}20,000=410^{-4}$$
Gravitational force $$ mg= 80
10^{-6}9.8=7.8410^{-4}N$$
Balancing the horizontal and vertical components of forces $$ T \sin \theta = F$$
$$ T\cos\theta=mg$$
where (T) is the tension in the thread
Now, $$ \tan\theta=\frac{F}{mg}=\frac{410^{-4}}{7.8410^{-4}}=0.51$$
Now, (\theta=27^\circ)
To find the tension T
$$ T=\sqrt{F^2+(mg)^2}=\sqrt{(410^{-4})^2+(7.8410^{-4})^2}=8.8*10^{-4}N$$

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