[2008EM/HMW-07]

IMSc-IV Physics-IV : Electricity and Magnetism Jan-Apr 2008 MM : 20 Set-VII : Tutorial-IV Electrostatic Energy, Motion in Electric Field

• Four charges $q,2q,-2q,-q$ are placed at the consecutive corners of a square of side $a$. Obtain expression for electrostatic energy of the charge system and compute its value for $q=1.5$ and $a=1$cm.
• A gold nucleus contains a positive charge equal to that of 79 protons. An $\alpha$ particle, $Z=2$, has kinetic energy $K$ at points far away from the nucleus and is travelling directly towards the charge, the particle just touches the surface of the charge and is reversed in direction. Relate $K$ to the radius of the gold nucleus and find the numerical value of kinetic energy in MeV if the radius $R$ is given to be $5 \times10^{-15} m$. \centerline {[ 1 MeV = $10^6$ eV and 1 eV = $1.6\times10^{-19}$J]}
• Two particles having equal masses of 5.0 g each and equal and opposite charges of $\pm 4.0 \times10^{-5}$ C are released from rest with a separation of 1.0m between them. Find the speeds of the particles when the separation is reduced to 50cm.
• Using the formula $$W=\frac{1}{2} \int \rho(\vec{r}) \phi(\vec{r}) d^3r $$ compute the electrostatic energy of a uniformly charged solid sphere having volume charge density $\rho$ and radius $R$.
• A block of mass $m$ and having charge $q$ is placed on a smooth horizontal table and is connected to a wall through a an unstressed spring of spring constant $k$ as shown in figure below. A horizontal electric field $E$ is switched on parallel to the spring Find the amplitude of resulting simple harmonic motion of the block.