Category: HC Verma Part 2: Electricity

Problem Statement A charge $q$ is placed at height $h$ above the centre of a square of side $2a$. Find the flux through the square. Given Information All quantities, constants, and constraints stated in the problem above Physical constants used as needed (see Concepts section) Physical Concepts & Formulas This problem draws on fundamental physical…

Problem Statement Determine the electric field for the configuration described: Determine the electric field for the configuration described: A sphere of radius $R$ has charge density $\rho(r) = \rho_0(1 – r/R)$. Find the total charge and the electric field at $r = R/2$. $Q = \int_0^R \rho(r)4\pi r^2 dr$; Gauss law for $E$ at $r…

Problem Statement A conducting sphere is placed in a uniform external electric field $E_0$. Describe the charge distribution and field pattern that results. Given Information All quantities, constants, and constraints stated in the problem above Physical constants used as needed (see Concepts section) Physical Concepts & Formulas This problem draws on fundamental physical principles. The…

Problem Statement A charge $q$ is placed at one vertex of a regular tetrahedron. Find the flux through each of the three faces adjacent to that vertex. Given Information All quantities, constants, and constraints stated in the problem above Physical constants used as needed (see Concepts section) Physical Concepts & Formulas This problem draws on…

Problem Statement Determine the electric field for the configuration described: Determine the electric field for the configuration described: The surface charge density on a conductor varies over its surface. At a certain point, $\sigma = 5\times10^{-6}$ C/m$^2$. Find the electric field at that point just outside the conductor. $E = \sigma/\varepsilon_0$ just outside conductor Given…

Problem Statement In a region, the electric field is $\vec{E} = (ax)\hat{i}$ N/C where $a = 200$ N/(C m). Find the volume charge density $\rho$ in this region. Given Information All quantities, constants, and constraints stated in the problem above Physical constants used as needed (see Concepts section) Physical Concepts & Formulas This problem draws…

Problem Statement Determine the electric field for the configuration described: Determine the electric field for the configuration described: Write the gravitational analog of Gauss’s law and use it to find the gravitational field inside the Earth (assumed uniform density $\rho$) at radius $r Gravitational Gauss: $\oint \vec{g}\cdot d\vec{A} = -4\pi G M_{enc}$ Step 1: Gaussian…

Problem Statement Determine the electric field for the configuration described: Determine the electric field for the configuration described: A conductor of irregular shape carries charge $Q$. Explain why all the charge resides on the outer surface, and why the field inside the conductor is zero. Free electrons rearrange until $E = 0$ inside conductor Gauss’s…

Problem Statement Two infinite parallel planes have surface charge densities $+\sigma$ and $+\sigma$. Find the electric field in all three regions: left, middle, and right. Given Information All quantities, constants, and constraints stated in the problem above Physical constants used as needed (see Concepts section) Physical Concepts & Formulas This problem draws on fundamental physical…

Problem Statement Determine the electric field for the configuration described: Determine the electric field for the configuration described: A solid sphere of radius $R$ has uniform charge density $\rho$. A spherical cavity of radius $R/2$ is scooped out with its centre at $R/2$ from the centre. Find the electric field at the centre of the…