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The line $A A^{\prime}$ is on charged infinite $A$ conducting plane which is perpendicular to the plane of the paper. The plane has a surface density of charge $\sigma$ and $B$ is ball of mass $m$ with a like charge of magnitude $q . B$ is connected by string from a point on the line $A A^{\prime}$. The tangent of angle (0) formed between the line $A A^{\prime}$ and the string is
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The correct answer is:
$\frac{q \sigma}{\varepsilon_{0} m g}$
The diagram is as follows
The electric field due to charged infinite conducting sheet is $E=\frac{\sigma}{\varepsilon_{0}}$
Now, force (electric force) on the charged ball is $F=q E=\frac{q \sigma}{\varepsilon_{0}}$
The resultant of electric force and $m g$ balance the tension produced in the string. So, tan $\theta=\frac{F_{e}}{m g}=\frac{q \sigma}{\frac{\varepsilon_{0}}{m g}}=\frac{q \sigma}{\varepsilon_{0} m g}$
The electric field due to charged infinite conducting sheet is $E=\frac{\sigma}{\varepsilon_{0}}$
Now, force (electric force) on the charged ball is $F=q E=\frac{q \sigma}{\varepsilon_{0}}$
The resultant of electric force and $m g$ balance the tension produced in the string. So, tan $\theta=\frac{F_{e}}{m g}=\frac{q \sigma}{\frac{\varepsilon_{0}}{m g}}=\frac{q \sigma}{\varepsilon_{0} m g}$
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