Help: I'm unable to solve an electrostatics problem.Could anyone please help me out?

Q-A small charged particle of mass m and charge q is suspended by an insulated thread in front of a very large sheet of charge density sigma. Then what is the angle made by the thread with the vertical in equilibrium?

#ElectricityAndMagnetism

Easy Math Editor

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Comments

Electric field from charge sheet (horizontal):

$E = \frac{\sigma}{2 \epsilon_0}$

Electric force (horizontal):

$F_e = q E = \frac{\sigma q}{2 \epsilon_0}$

Gravitational force (vertical):

$F_g = m g$

Rope tension components ( $\theta$ is angle with vertical):

$T \, cos \theta = m g \\ T \, sin \theta = \frac{\sigma q}{2 \epsilon_0} \\ tan \theta = \frac{\sigma q}{2 \epsilon_0 m g}$

Steven Chase - 3 years, 1 month ago

Thanks a lot!

Shreeram Petkar - 3 years, 1 month ago

Sure thing

Steven Chase - 3 years, 1 month ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$