Category: HC Verma Part 2: Electricity

Problem Statement A spherical shell of radius $R$ has charge $Q$ on it. A charge $q$ is placed at the centre. Find the electric field (a) inside the shell, and (b) outside the shell. Given Information All quantities, constants, and constraints stated in the problem above Physical constants used as needed (see Concepts section) Physical…

Problem Statement An infinite plane has charge density $\sigma = 2\times10^{-6}$ C/m$^2$. Find the electric field on both sides. 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 to identify…

Problem Statement A Gaussian surface has zero net flux. Does this mean (a) the electric field is zero at every point, or (b) the net charge inside is zero? Explain. 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 Statement Determine the electric field for the configuration described: Determine the electric field for the configuration described: A point charge $q = 5\times10^{-8}$ C is placed at the centre of a sphere of radius 10 cm. Find (a) the total flux through the sphere, and (b) the flux through any small area element $\Delta…

Problem Statement Find the electric flux through a closed surface enclosing charges $+3\mu$C, $-2\mu$C, and $+1\mu$C. 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 to identify which conservation law…

Problem Statement Solve the capacitor/capacitance problem: Solve the capacitor/capacitance problem: Three capacitors of $2\mu$F, $3\mu$F, and $6\mu$F are connected in series. Find (a) the equivalent capacitance, and (b) the charge on each capacitor when connected to a 12 V battery. Series: $1/C_{eq} = 1/C_1 + 1/C_2 + 1/C_3$ Same charge on each capacitor in Given…

Problem Statement Determine the electric field for the configuration described: Determine the electric field for the configuration described: A parallel plate capacitor has plate separation 2 mm and voltage 500 V. Find the energy density in the electric field between the plates. Energy density: $u = \frac{1}{2}\varepsilon_0 E^2$ $E = V/d$ Step 1: $E =…

Problem Statement Solve the kinematics problem: Solve the kinematics problem: In a velocity selector, a uniform electric field $E = 3\times10^4$ N/C and a magnetic field $B = 0.3$ T are crossed. Find the speed of particles that pass through undeflected. At balance: electric force = magnetic force, $qE = qvB$ Step 1: For undeflected…

Problem Statement Solve the capacitor/capacitance problem: A parallel plate capacitor with plate area $A$ carries charge density $\sigma$. Find the attractive force between the plates. Each plate produces field $\sigma/(2\varepsilon_0)$ Force = (charge on one plate) $\times$ (field due to other plate) Step 1: Field due to one plate: $E_{half} = \sigma/(2\va Given Information See…

Problem Statement Solve the capacitor/capacitance problem: A $3\mu$F capacitor charged to 100 V is connected in parallel with an uncharged $6\mu$F capacitor. Find the common potential and the energy lost. Charge conservation: $Q_{total} = (C_1+C_2)V_f$ Energy lost = initial energy – final energy Step 1: Initial charge $Q = C_1 V_0 = 3\times10^{-6}\times100 Given Information…