1. Tardigrade
  2. Question
  3. Physics
  4. The line A A' is on charged infinite. A conducting plane which is perpendicular to the plane of the paper. The plane has a surface density of charge σ and B is ball of A' mass m with a like charge of magnitude q. B is connected by string from a point on the line A A'. The tangent of angle (θ) formed between the line A A' and the string is

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. The line $A A'$ 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 $A'$ mass $m$ with a like charge of magnitude q. $B$ is connected by string from a point on the line $A A'$. The tangent of angle $(\theta)$ formed between the line $A A'$ and the string isPhysics Question Image

WBJEEWBJEE 2015

Solution:

The diagram is as follows
image
The electric field due to charged infinite conducting sheet is
$E=\frac{\sigma}{\varepsilon_{0}}$.
Now, force (electric force) on the charged ball is
$F =q E=\frac{q_{0}}{\varepsilon_{0}}$
The resultant of electric force and $m g$ balance the tension produced in the string. So, $\tan \theta=\frac{F_{\theta}}{m g}$
$=\frac{q \sigma}{\frac{\varepsilon_{0}}{m g}}=\frac{q \sigma}{\varepsilon_{0} m g}$