Two charges $q$ and $3q$ are separated by a distance $r$ in air. At a distance $x$ from charge $q$,the resultant electric field is zero. The value of $x$ is:

Why is an electric force conservative?

$A$ uniformly charged semicircular arc of radius $r$ has linear charge density $\lambda$. What is the electric field at its centre? $(\epsilon_0 = \text{permittivity of free space})$

Is electric field a scalar or a vector quantity? Why?

Two point charges $+10 q$ and $-4 q$ are located at $x=0$ and $x=L$ respectively. What is the location of a point on the $x$-axis from the origin, where the net electric field due to these two point charges is zero? $(r = \text{required distance})$

$A$ cube of side $L$ has point charges $+q$ located at its seven vertices and $-q$ at remaining one vertex. The electric field at its centre is found to be $|E|=\alpha\left(\frac{q}{4 \pi \varepsilon_0 L^2}\right)$. The magnitude of constant $\alpha$ is