The circular wire in figure below encircles solenoid in which the magnetic flux is increasing at a constant rate out of the plane of the page. The clockwise emf around the circular loop is $\varepsilon_{0}$. By definition a voltammeter measures the voltage difference between the two points given by $V_{b}-V_{a}=-\int \limits_{a}^{b} E \cdot d s$ We assume that $a$ and $b$ are infinitesimally close to each other. The values of $V_{b}-V_{a}$ along the path $1$ and $V_{a}-V_{b}$ along the path $2$ , respectively are

The electric field in a certain region is acting radially outward and is given by $E =Ar.$ A charge contained in a sphere of radius $'a'$ centred at the origin of the field, will be given by

${q_1},\;{q_2},\;{q_3}$ 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

A point charge $+10\; \mu \,C$ is a distance $5 cm$ directly above the centre of a square of side $10 \;cm ,$ as shown in Figure. What is the magnitude of the electric flux through the square?

A linear charge having linear charge density $\lambda$ , penetrates a cube diagonally and then it penetrate a sphere diametrically as shown. What will be the ratio of flux coming cut of cube and sphere

A disk of radius $a / 4$ having a uniformly distributed charge $6 \mathrm{C}$ is placed in the $x-y$ plane with its centre at $(-a / 2,0,0)$. A rod of length $a$ carrying a uniformly distributed charge $8 \mathrm{C}$ is placed on the $x$-axis from $x=a / 4$ to $x=5 a / 4$. Two point charges $-7 \mathrm{C}$ and $3 \mathrm{C}$ are placed at $(a / 4,-a / 4,0)$ and $(-3 a / 4,3 a / 4,0)$, respectively. Consider a cubical surface formed by six surfaces $x= \pm a / 2, y= \pm a / 2$, $z= \pm a / 2$. The electric flux through this cubical surface is