Figure shows the electric field lines around three point charges $A, \,B$ and $C$.
$(a)$ Which charges are positive ?
$(b)$ Which charge has the largest magnitude ? Why ?
$(c)$ In which region or regions of the picture could the electric field be zero ? Justify your answer.
$(i)$ Near $A$ $(ii)$ Near $B$ $(iii)$ Near $C$ $(iv)$ Nowhere
$(i)$ Electric field lines of $A$ and $C$ are outwards. Hence, charges of $A$ and $C$ are positive.
$(ii)$ No. of Electric field lines from $C$ is maximum. Hence, magnitude of charge $C$ is maximum.
$(iii)$ Electric field lines of like charges are opposite to each other. Hence, the electric field can be zero between $\mathrm{A}$ and $\mathrm{C}$ only.
The magnitude of charge at $\mathrm{C}$ is greater than that at $\mathrm{A}$. Hence, the electric field is zero at point near $A.$
How does the no. of electric field lines passing through unit area depend on distance ?
${q_1},\;{q_2},\;{q_3}$ and ${q_4}$ are point charges located at points as shown in the figure and $S$ is a spherical Gaussian surface of radius $R$. Which of the following is true according to the Gauss’s law
The electric field components in Figure are $E_{x}=\alpha x^{1 / 2}, E_{y}=E_{z}=0,$ in which $\alpha=800 \;N / C\, m ^{1 / 2} .$ Calculate
$(a)$ the flux through the cube, and
$(b)$ the charge within the cube. Assume that $a=0.1 \;m$
Gauss’s law is true only if force due to a charge varies as
A charge of $1$ coulomb is located at the centre of a sphere of radius $10 \,cm$ and a cube of side $20 \,cm$. The ratio of outgoing flux from the sphere and cube will be