Category: HC Verma Part 2: Electricity

Problem Statement A charge $q$ is placed at the midpoint of one edge of a cube. Find the flux through each face of the cube. 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 The electric field in a region is $\vec{E} = E_0(x/a)\hat{i}$, where $E_0$ and $a$ are constants. Find the charge enclosed in a cube of side $a$ with one corner at the origin. Given Information All quantities, constants, and constraints stated in the problem above Physical constants used as needed (see Concepts section) Physical…

Problem Statement The electric flux through a closed surface is measured to be $5.0\times10^4$ N m$^2$/C. Find the net charge enclosed. 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 key is…

Problem Statement Determine the electric field for the configuration described: Determine the electric field for the configuration described: A solid cylinder of radius $R$ carries uniform volume charge density $\rho$. Find the electric field at distance $r$ from the axis for $r R$. Cylindrical Gauss law Inside ($r Enclosed charge per unit length: $\rho\pi r^2$.…

Problem Statement Determine the electric field for the configuration described: Determine the electric field for the configuration described: Use Gauss’s law to derive Coulomb’s law for the electric field of a point charge $q$. Spherical Gaussian surface centred on $q$; spherical symmetry Step 1: By symmetry, $\vec{E}$ is radial and constant in magnitude on a…

Problem Statement An infinite slab of thickness $2a$ has uniform volume charge density $\rho$. Find the electric field (a) inside the slab at distance $x$ from the midplane, and (b) outside the slab. Given Information All quantities, constants, and constraints stated in the problem above Physical constants used as needed (see Concepts section) Physical Concepts…

Problem Statement A charge $q$ is placed at the centre of a sphere of radius $R$. Find the flux through a hemisphere (half the sphere). 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 A conducting sphere of inner radius 5 cm and outer radius 8 cm has a charge of $+10\mu$C placed at its centre cavity. The sphere itself carries $+4\mu$C. Find the charge on (a) the inner surface, (b) the outer surface. Given Information All quantities, constants, and constraints stated in the problem above Physical…

Problem Statement Determine the electric field for the configuration described: Determine the electric field for the configuration described: A coaxial cable has inner conductor of radius $a$ (charge per unit length $+\lambda$) and outer conductor of radius $b$ (grounded). Find the field in the region $a Cylindrical Gauss law Step 1: Gaussian cylinder of radius…

Problem Statement An infinite cylindrical shell of radius $R$ carries surface charge density $\sigma$. Find the field (a) outside and (b) inside the cylinder. 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.…