The linear charge density upon the semi-circular ring, on both side is same in magnitude, the electric field at $O$ is along

An infinite long thread carries a charge uniformly spread over its length. It is bent in the form as shown. If the charge per unit length is $\lambda$, the electric field at point $O$ is

An infinitely large non-conducting plane sheet of charge density $\sigma$ has a circular aperture of certain radius carved out of it. The electric field at a point which is at a distance $\text{'}a\text{'}$ from the centre of aperture is $\frac{\sigma }{2\sqrt{2}{\epsilon }_0}.$ The radius of aperture is

The electric field due to charged circular arc shown in following figure, at centre $O$ is

If $\lambda =1\mu \mathrm{C} {\mathrm{m}}^{–1}$, then electric field intensity at $O$ is

A test charge $q_0$ is placed in the electric field of a source charge $Q.$ The test charge will not follow path of electric field line if