Question

A pith ball of mass $m$ grams and charge $Q$ is suspended using a massless silk thread near a large charged conducting metal sheet of area $A$ and surface charge density $\sigma$. If the silk thread makes an angle $\theta$ with the metal sheet, then $\tan\theta$ is equal to:

• A. $\frac{Q\sigma}{2\varepsilon_0 mg}$
• B. $\frac{Q\sigma}{\varepsilon_0 mg}$
• C. $\frac{Q\sigma}{2A\varepsilon_0 mg}$
• D. $\frac{\varepsilon_0 mg}{Q\sigma}$

Hint:

Be careful not to confuse a charged conducting sheet ($E = \frac{\sigma}{\varepsilon_0}$) with a thin non-conducting infinite sheet ($E = \frac{\sigma}{2\varepsilon_0}$). The problem specifies a conducting metal plate, which establishes twice the field strength!

Answer 1

The Correct Option is B