A particle of mass $2 \mathrm{kg}$ and charge $1 \mathrm{mC}$ is projected vertically with a velocity $10 \mathrm{m} {\mathrm{s}}^{-1}$. There is a uniform horizontal electric field of ${10}^4 \mathrm{N} {\mathrm{C}}^{-1}$. Select the incorrect statement.

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 $\alpha$.

Consider a regular cube with positive point charge $+Q$ at all corners except for one which has a negative point charge $-Q$. Let the distance from any corner to the centre of the cube be $r$. What is the magnitude of the electric field at point $P$, the centre of the cube?

A particle of charge $-q$ and mass $m$ moves in a circle of radius $r$ around an infinitely long line charge of linear charge density $+\lambda .$ Then, the time period of revolution of the particle will be $\left(k=\frac{1}{4\pi {\epsilon }_0}\right)$,