Category: HC Verma Part 2: Electricity

Problem Statement A charge $+Q$ is placed at the centre of a grounded conducting spherical shell of inner radius $a$ and outer radius $b$. Find the charge distribution and potential of the shell. Given Information See problem statement for all given quantities. Physical Concepts & Formulas This problem applies fundamental physics principles to the scenario…

Problem Statement A shell of radius $R_1$ carries charge $Q_1$ and is surrounded by a shell of radius $R_2$ carrying charge $Q_2$. Find the potential at the surface of the inner shell. Given Information See problem statement for all given quantities. Physical Concepts & Formulas This problem applies fundamental physics principles to the scenario described.…

Problem Statement Show that the electric potential is constant throughout the volume of a conductor in electrostatic equilibrium. Given Information See problem statement for all given quantities. Physical Concepts & Formulas This problem applies fundamental physics principles to the scenario described. The solution requires identifying the relevant conservation laws and equations of motion, then solving…

Problem Statement Show that the electric field just outside the surface of a conductor is $E = \sigma/\varepsilon_0$, where $\sigma$ is the surface charge density. Given Information See problem statement for all given quantities. Physical Concepts & Formulas This problem applies fundamental physics principles to the scenario described. The solution requires identifying the relevant conservation…

Problem Statement Determine the electric field for the configuration described: Find the electric field at a perpendicular distance $r$ from an infinitely long straight wire carrying uniform linear charge density $\lambda$. Gauss’s law with a cylindrical Gaussian surface $\oint \vec{E}\cdot d\vec{A} = Q_{enc}/\varepsilon_0$ Step 1: Choose a coaxial cylinder of radius $r$ and le Given…

Problem Statement A ring of radius $R$ carries a total charge $Q$. Find the electric potential at a point P on the axis at distance $x$ from the centre of the ring. Given Information See problem statement for all given quantities. Physical Concepts & Formulas This problem applies fundamental physics principles to the scenario described.…

Problem Statement Solve the work-energy problem: Show that no work is done in moving a charge along an equipotential surface. Work done: $W = q(V_A – V_B)$ On an equipotential surface, $V_A = V_B$ Step 1: An equipotential surface is defined as a surface where the electric potential $V$ is the same at every point.…

Problem Statement A uniform electric field $E = 1000$ N/C exists in the $x$-direction. A square of side 10 cm is placed in the $yz$-plane. Find the electric flux through the square. Given Information See problem statement for all given quantities. Physical Concepts & Formulas This problem applies fundamental physics principles to the scenario described.…

Problem Statement Determine the electric field for the configuration described: An electric dipole of moment $p$ and moment of inertia $I$ is placed in a uniform electric field $E$. Show that for small angular displacements it executes SHM, and find the time period. Restoring torque for small $\theta$: $\tau = -pE\sin\theta \approx -pE\theta$ Angular equation:…

Problem Statement Solve the work-energy problem: An electric dipole of moment $p = 5\times10^{-8}$ C m is placed in a uniform electric field $E = 2\times10^4$ N/C. Find the potential energy when (a) $\theta = 0°$, (b) $\theta = 90°$, (c) $\theta = 180°$. $U = -pE\cos\theta$ Given: $pE = 5\times10^{-8} \times 2\times10^4 = 10^{-3}$…