The figure shows a cross-section of two solid spheres with uniformly distributed charge throughout their volumes. Each has a radius $R.$ Point $P$ lies on a line connecting the centers of the spheres, at a radial distance $\frac{R}{4.00}$ from the center of the sphere $1$. If the net electric field at point $P$ is zero, what is the ratio $\frac{q_2}{q_1}$ of the total charges?

The figure shows a closed Gaussian surface in the shape of a cube of edge length $1.50 \mathrm{m}$ . It lies in a region where the nonuniform electric field is given by $\overrightarrow{E}=\left(3.00x+4.00\right)\hat{\mathrm{i}}+6.00\hat{\mathrm{j}}+7.00\hat{\mathrm{k}} \mathrm{N} {\mathrm{C}}^{-1}$ with $x$ in meters. What is the net charge contained by the cube?

The square surface shown in the figure, measures $6.8 \mathrm{mm}$ on each side. It is immersed in a uniform electric field with magnitude $E=1800 \mathrm{N} {\mathrm{C}}^{-1}$ and with field lines at an angle of $\theta =35°$ with a normal to the surface, as shown. Take that normal to be directed outward, as though the surface were one face of a box. $\left(a\right)$ Calculate the electric flux through the surface. $\left(b\right)$ If the angle is reduced by a few degrees, does the flux increases or decreases or remains same.

The figure shows a cross-section through a very large nonconducting slab of thickness $d=9.40 \mathrm{mm}$ and uniform volume charge density $\rho =1.89 \mathrm{fC} {\mathrm{m}}^{-3}.$ The origin of an $x$-axis is at the slab's center. What is the magnitude of the slab's electric field at an $x$-coordinate of $\left(a\right)$ $0$ $\left(b\right)$ $2.00 \mathrm{mm}$ $\left(c\right)$ $4.70 \mathrm{mm},$ and $\left(d\right)$ $26.0 \mathrm{mm}?$

The figure shows two nonconducting spherical shells fixed in place. Shell $1$ has uniform surface charge density $+6.0 \mu \mathrm{C} {\mathrm{m}}^{-2}$ on its outer surface and radius $3.0 \mathrm{cm}$; shell $2$ has uniform surface charge density $+4.0 \mu \mathrm{C} {\mathrm{m}}^{-2}$ on its outer surface and radius $2.0 \mathrm{cm}$ the shell centers are separated by $L=12 \mathrm{cm}.$ In unit-vector notation, what is the net electric field at $x=2.0 \mathrm{cm}?$