Category: HC Verma Part 2: Electricity

Problem Statement A Van de Graaff generator has a sphere of radius 1.0 m. Find (a) the maximum potential the sphere can be raised to (breakdown field of air = $3\times10^6$ N/C), and (b) the charge at that potential. Given Information See problem statement for all given quantities. Physical Concepts & Formulas This problem applies…

Problem Statement Solve the work-energy problem: A conducting shell of radius $R_1$ with charge $Q_1$ is placed inside a conducting shell of radius $R_2$ with charge $Q_2$. Find the electrostatic energy of the system. Energy = $\frac{1}{2}\int\varepsilon_0 E^2\,dV$ over all space Regions: $r R_2$ Step 1: $E = 0$ for $r R_2$. Step 2: $U…

Problem Statement A conductor has a cavity inside. An external field $E_0$ exists. Show that (a) $E = 0$ inside the cavity, and (b) the cavity is shielded from external fields. Given Information See problem statement for all given quantities. Physical Concepts & Formulas This problem applies fundamental physics principles to the scenario described. The…

Problem Statement Solve the nuclear physics problem: In the Bohr model of hydrogen, the electron orbits at $a_0 = 0.529$ Angstrom. Find the potential energy, kinetic energy, and total energy of the electron. Circular orbit: $ke^2/r^2 = mv^2/r$ $KE = \frac{1}{2}mv^2 = ke^2/(2r)$ $PE = -ke^2/r$ Step 1: $r = 0.529\times10^{-10}$ m, $e = 1.6\times10^{-19}…

Problem Statement Solve the work-energy problem: A charge of $2\mu$C is moved from a point where potential is 100 V to a point where potential is 20 V. Find the work done by the external agent and by the electric force. Work by external agent: $W_{ext} = q(V_B – V_A)$ Work by electric force: $W_E…

Problem Statement Determine the electric field for the configuration described: Find the electric field at a point on the axis of a uniformly charged ring of radius $R$ carrying total charge $Q$, at distance $x$ from the centre. Also find where the field is maximum. By symmetry, only the axial component survives $E = \dfrac{kQx}{(R^2+x^2)^{3/2}}$…

Problem Statement A charge $q$ is placed between two large parallel plates separated by distance $d$. One plate has charge density $+\sigma$ and the other $-\sigma$. Find the force on $q$. Given Information See problem statement for all given quantities. Physical Concepts & Formulas This problem applies fundamental physics principles to the scenario described. The…

Problem Statement In a Millikan-type experiment, a charged oil drop of mass $m = 1.6\times10^{-14}$ kg is held stationary in a vertical electric field $E = 2.45\times10^4$ N/C. Find the charge on the drop. Given Information See problem statement for all given quantities. Physical Concepts & Formulas This problem applies fundamental physics principles to the…

Problem Statement Determine the electric field for the configuration described: A solid non-conducting sphere of radius $R$ carries uniform volume charge density $\rho$. Find the electric field at distance $r$ from the centre for both $r R$. Gauss’s law: $E\cdot4\pi r^2 = Q_{enc}/\varepsilon_0$ Outside ($r > R$): $$Q_{enc} = \frac{4}{3}\pi R^3\rho$$ $$E = \frac{\rho R^3}{3\vare…

Problem Statement Solve the capacitor/capacitance problem: A parallel plate capacitor has plates of area $2A$ and separation $d$. The left half ($A$) is filled with dielectric $K_1$ and the right half ($A$) with dielectric $K_2$. Find the total capacitance. Two capacitors in parallel: $C = C_1 + C_2$ Step 1: $C_1 = K_1\varepsilon_0 A/d$ and…