Category: HC Verma Part 2: Electricity

Problem Statement Solve the rotational mechanics problem: An electric dipole of moment $1.0\times10^{-8}$ C m is placed in a uniform electric field of magnitude $1.0\times10^4$ N/C. Find the torque when the dipole makes angle $30°$ with the field direction. Torque on dipole: $\tau = pE\sin\theta$ Step 1: $p = 1.0\times10^{-8}$ C m, $E = 1.0\times10^4$…

Problem Statement Charges $q_1 = 2.0\times10^{-6}$ C and $q_2 = -4.0\times10^{-6}$ C are placed 20 cm apart. Find the point on the line joining them where the electric field is zero. 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 Determine the electric field for the configuration described: Two charges $+3.2\times10^{-19}$ C and $-3.2\times10^{-19}$ C are placed 2.4 Angstrom apart forming a dipole. Find the electric field at a point 4.0 cm from the centre on the axis of the dipole. Dipole moment: $p = qd$ Axial electric field (for $r \gg d$):…

Problem Statement Determine the electric field for the configuration described: Charges $+q$ and $-q$ are placed at points A and B, $2d$ apart. Find the electric field at the midpoint O of AB. Superposition principle for electric fields Step 1: Distance from each charge to O is $d$. Step 2: Field at O due to…

Problem Statement Determine the electric field for the configuration described: A particle is given a charge of $0.2\times10^{-6}$ C and placed in an electric field of $3000$ N/C. Find the electric force on the particle. $F = qE$ Step 1: $q = 2.0\times10^{-7}$ C, $E = 3000$ N/C. Step 2: $$F = qE = 2.0\times10^{-7}…

Problem Statement Determine the electric field for the configuration described: Find the electric field due to a charge of $4.0\times10^{-6}$ C at a distance of 1.0 m from it. Electric field: $E = \dfrac{kq}{r^2}$ Step 1: $q = 4.0\times10^{-6}$ C, $r = 1.0$ m, $k = 9\times10^9$ N m$^2$/C$^2$. Step 2: $$E = \frac{9\times10^9 \times…

Problem Statement Two identical balls, each having charge $q$ and mass $m$, are suspended from a common point by strings of length $L$. At equilibrium each string makes angle $\theta$ with the vertical. Find the charge $q$. Given Information See problem statement for all given quantities. Physical Concepts & Formulas This problem applies fundamental physics…

Problem Statement Three equal charges $q$ are placed at the three corners of an equilateral triangle of side $a$. Find the net force on any one charge due to the other two. 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 Newton’s Laws / mechanics problem: Two equal charges are placed at a separation of 1.0 m. What is the charge if the Coulomb force between them is 0.1 N? Coulomb’s Law for equal charges: $F = \dfrac{kq^2}{r^2}$ Step 1: Given $F = 0.1$ N, $r = 1.0$ m, $k = 9\times10^9$…

Problem Statement Solve the Newton’s Laws / mechanics problem: Find the electric force between two protons separated by a distance of 1 fermi (1 fm = 10 -15 m). Coulomb’s Law: $F = \dfrac{kq_1 q_2}{r^2}$ Charge of proton: $q = 1.6 \times 10^{-19}$ C $k = 9 \times 10^9$ N m$^2$/C$^2$ Step 1: Given: $q_1…