A thin semi-circular ring of radius $r$ has a positive charge $q$ distributed uniformly over it. The net field $\overrightarrow{E}$ at the centre $O$ is,

Two semicircular rings lying in same plane and of a uniform linear charge density $\lambda$ have radii $r$ and $2r$. They are joined using two straight uniformly charged wires of linear charge density $\lambda$ and length $r$ as shown in the figure. The magnitude of electric field at common centre of semi-circular rings is,

An infinitely long wire, having uniform linear charge density $\frac{10}{9} \mathrm{nC} {\mathrm{m}}^{-1}$ is kept along $z$-axis from $z=-\infty$ to $z=+\infty$. The electric field $\overrightarrow{E}$ at point $(6 \mathrm{cm}, 8 \mathrm{cm},10 \mathrm{cm})$ will be,

Find the magnitude of uniform electric field $E$ (in $\mathrm{N} {\mathrm{C}}^{-1}$ ) (direction shown in figure) if an electron entering with velocity $100 \mathrm{m} {\mathrm{s}}^{-1}$ and making $30°$ with $x$-axis comes out making $60°$ with $x$-axis after a time numerically equal to $\frac{m}{e}$ of electron.

Two mutually perpendicular wires carry charge densities ${\lambda }_1$ and ${\lambda }_2$. If the electric line of force makes an angle $\alpha$ with the second wire, then find $\frac{{\lambda }_1}{{\lambda }_2}$ in terms of angle $\alpha$.