Category: HC Verma Part 2: Electricity

Problem Statement Find the electric field at a point on the equatorial line (perpendicular bisector) of an electric dipole of moment $p$, at distance $r$ from the centre (for $r \gg d$). Given Information See problem statement for all given quantities. Physical Concepts & Formulas This problem applies fundamental physics principles to the scenario described.…

Problem Statement An electric dipole of moment $p$ is placed in a non-uniform electric field. Show that the net force on the dipole is $F = p\,\dfrac{dE}{dx}$ (for dipole aligned along the field). Given Information See problem statement for all given quantities. Physical Concepts & Formulas This problem applies fundamental physics principles to the scenario…

Problem Statement Determine the electric field for the configuration described: A proton is released from rest in a uniform electric field of $100$ N/C. Find (a) the acceleration, and (b) the speed after it has travelled 1.0 m. $F = qE$, $a = F/m$ Kinematics: $v^2 = u^2 + 2as$ Proton: $q = 1.6\times10^{-19}$ C,…

Problem Statement Solve the work-energy problem: Three charges $q$, $q$, and $-2q$ are placed at the vertices of an equilateral triangle of side $a$. Find the potential energy of the system. Total potential energy = sum over all pairs: $U = \sum_{pairs} \dfrac{kq_i q_j}{r_{ij}}$ Step 1: Three pairs: $(q,q)$, $(q,-2q)$, $(q,-2q)$. All separations = Given…

Problem Statement A uniformly charged sphere of radius $R$ carries total charge $Q$. Find the electric potential at (a) the surface, and (b) the centre. Given Information See problem statement for all given quantities. Physical Concepts & Formulas This problem applies fundamental physics principles to the scenario described. The solution requires identifying the relevant conservation…

Problem Statement Determine the electric field for the configuration described: The electric potential in a region is $V = 2x^2 – 3y$. Find the electric field at the point $(2, 3)$. $E_x = -\dfrac{\partial V}{\partial x}$, $E_y = -\dfrac{\partial V}{\partial y}$ Step 1: $V = 2x^2 – 3y$ Step 2: $E_x = -\dfrac{\partial V}{\partial x}…

Problem Statement A ring of radius $R$ carries a total charge $Q$. Find the electric potential at a point P on the axis at distance $x$ from the centre of the ring. Given Information See problem statement for all given quantities. Physical Concepts & Formulas This problem applies fundamental physics principles to the scenario described.…

Problem Statement Two point charges $+q$ and $-q$ are separated by distance $2a$. Describe the equipotential surfaces and find the potential at the midpoint. Given Information See problem statement for all given quantities. Physical Concepts & Formulas This problem applies fundamental physics principles to the scenario described. The solution requires identifying the relevant conservation laws…

Problem Statement Find the electric potential at the midpoint between two charges $+2\mu$C and $-2\mu$C separated by 1.0 m. Given Information See problem statement for all given quantities. Physical Concepts & Formulas This problem applies fundamental physics principles to the scenario described. The solution requires identifying the relevant conservation laws and equations of motion, then…

Problem Statement Solve the work-energy problem: Two charges of $4.0 \times 10^{-6}$ C each are separated by a distance of 0.5 m. Find the electric potential energy of the system. Electric potential energy: $U = \dfrac{kq_1 q_2}{r}$ Step 1: $q_1 = q_2 = 4.0 \times 10^{-6}$ C, $r = 0.5$ m. Step 2: $$U =…