Question

A small sphere of mass $m$ and having charge $q$ is suspended by a silk thread of length $l$ in a uniform horizontal electric filed. If it stands at a distance x from the vertical line from point of suspension, then magnitude of electric field is, as per the figure

• A. $\frac{mg}{q}$
• B. $\frac{mg}{q}\frac{x}{l}$
• C. $\frac{mgx}{q\sqrt{l^2-x^2}}$
• D. $\frac{mgl}{q\sqrt{x^2-l^2}}$

Answer 1

The correct option is

C

$\frac{mgx}{q\sqrt{l^2-x^2}}$

$E=?$

the distance $=\sqrt{l^2-x^2}$

$E_q\sqrt{l^2-x^2}=mgx$

where $mg$ is equivalent to $E$

now,

or, $E=\frac{mgx}{q\sqrt{l^2-x^2}}$