Question

A small charged particle of mass 'm' and charge q is suspended by an insulated thread in front of a very large conducting charged sheet of surface density of charge σ. The angle made by the thread with the vertical in equilibrium is

• A. tan^-1$\left( \frac{\sigma q}{2\varepsilon_{0}mg} \right)$
• B. tan^-1$\left( \frac{\sigma}{q\varepsilon_{0}mg} \right)$
• C. tan^-1$\left( \frac{q}{2\sigma\varepsilon_{0}mg} \right)$
• D. zero

Answer 1

Answer: (A)

tan^-1$\left( \frac{\sigma q}{2\varepsilon_{0}mg} \right)$

Answer 2

In equilibrium, along x - axis, Tsinθ = qE

⇒ T sinθ = q $\frac{\sigma}{2\varepsilon_{0}}$ ........ (1)

Where T is the tension in the string. Along y-axis in equilibrium,

Tcosθ = mg ....... (2)

From (1) and (2) we obtain

tanθ = $\frac{q\sigma}{2\varepsilon_{0}mg}$ ⇒ θ = tan^-1 $\left( \frac{\sigma q}{2\varepsilon_{0}mg} \right)$