Question

A finite line charge has $-Q$ uniformly distributed on upper half and $+Q$ uniformly distributed on lower half as shown.
Find the direction of electric field at point $\text{P}.$

• A. Along positive $x-$ axis
• B. Along ngative $x-$ axis
• C. Along positive $y-$ axis
• D. Along ngative $y-$ axis

Answer 1

The correct option is C Along positive $y-$ axis

Consider two elemental charges of magnitude $\left(dq\right)$ each symmetrical about x-axis


Due to $+dq$ charge magnetic field acts away from it and due to $-dq$ charge, magnetic field acts towards it as shown in above figure.

From the above figure, we can say that $x-$ components of electric field intensity will cancel each other and $y-$ components will be added.
Hence, net electric field directed towards $+y$-axis.