The charge density of a uniformly charged inf | vedclass

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(C) For a simple pendulum in equilibrium under the influence of an electric field $E$ produced by an infinite charged plane,the forces acting on the b

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$\sigma \propto 	an 	heta$

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(C) For a simple pendulum in equilibrium under the influence of an electric field $E$ produced by an infinite charged plane,the forces acting on the bob are tension $T$,gravitational force $mg$,and electrostatic force $F_e = q_0 E$.Resolving the forces into horizontal and vertical components:$T \sin 	heta = q_0 E$$T \cos 	heta = mg$Dividing the two equations:$	an 	heta = \frac{q_0 E}{mg}$The electric field due to a uniformly charged infinite plane is given by:$E = \frac{\sigma}{2 \varepsilon_0}$Substituting this into the expression for $	an 	heta$:$	an 	heta = \frac{q_0}{mg} \left( \frac{\sigma}{2 \varepsilon_0} ight)$Since $q_0$,$m$,$g$,and $\varepsilon_0$ are constants,we have:$	an 	heta \propto \sigma$Or,$\sigma \propto 	an 	heta$.

The charge density of a uniformly charged infinite plane is $\sigma$. $A$ simple pendulum is suspended vertically downward near it. $A$ charge $q_0$ is placed on the metallic bob. If the angle made by the string with the vertical direction is $\theta$,then . . . . . . .

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