The electric field at $20 \,cm$ from the centre of a uniformly charged non-conducting sphere of radius $10 \,cm$ is $E$. Then at a distance $5 \,cm$ from the centre it will be

An electric field converges at the origin whose magnitude is given by the expression $E = 100\,r\,N/C$,where $r$ is the distance measured from the origin.

Find the ratio of the electric field at points $A$ and $B$. An infinitely long uniformly charged wire with linear charge density $\lambda$ is kept along the $z$-axis.

An infinitely long solid cylinder of radius $R$ has a uniform volume charge density $\rho$. It has a spherical cavity of radius $R/2$ with its centre on the axis of the cylinder,as shown in the figure. The magnitude of the electric field at the point $P$,which is at a distance $2R$ from the axis of the cylinder,is given by the expression $\frac{23\rho R}{16K\varepsilon_0}$. The value of $K$ is

The electric field components in the figure are $E_{x}=\alpha x^{1 / 2}, E_{y}=E_{z}=0,$ in which $\alpha=800 \; N/C \cdot m^{1/2}.$ Calculate
$(a)$ the flux through the cube,and
$(b)$ the charge within the cube. Assume that $a=0.1 \; m$.

$A$ non-conducting solid sphere of radius $R$ is uniformly charged. The magnitude of the electric field due to the sphere at a distance $r$ from its centre: