Question

For the given uniformly charged ring sector symmetrically placed about $Y$ axis, net electric filed at the point $\text{P}$ along $X$-direction is
$[l$ is the length of the arc, $\lambda$ is linear charge density, $R$ is radius of sector$]$

• A. $\frac{2k\lambda }{R}\sin \left(\frac{l}{2R}\right)$
• B. $\frac{2k\lambda }{R}\sin \left(\frac{l}{R}\right)$
• C. $\frac{2k\lambda }{R}$
• D. Zero

Answer 1

The correct option is D Zero


As shown in the above figure, for every small charge element $\left(dQ\right)$ on the right side of $\text{PA}$, there is another symmetrical small charge element $\left(dQ\right)$ on the left side of $\text{PA}$ at the ring sector whose $Y-$ components get added but there $X-$ components cancel each other.

Therefore, the net electric field due to whole ring sector in $X$-direction is zero by symmetry.

So, $\left(d\right)$ is the correct option.