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# 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 $$F=qE=2*10^{-8}*20,000=4*10^{-4}$$
Gravitational force $$mg= 80*10^{-6}*9.8=7.84*10^{-4}N$$
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, $$\tan\theta=\frac{F}{mg}=\frac{4*10^{-4}}{7.84*10^{-4}}=0.51$$
Now, $$\theta=27^\circ$$
To find the tension T
$$T=\sqrt{F^2+(mg)^2}=\sqrt{(4*10^{-4})^2+(7.84*10^{-4})^2}=8.8*10^{-4}N$$

September 17, 2017

## Checking irreducibility over $$\mathbb{R}$$ (TIFR 2013 problem 37)

© Cheenta 2017

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