[2008EM/HMW-01]

IMSc-IV Physics-IV : Electricity and Magnetism Jan-Apr 2008 MM : 20
Set-II : Tutorial-I
    Coulomb’s Law     

            [$\oslash$] In numerical problems compute the final numbers upto three significant places.
            [$\oslash$] Give your answer in SI units only. Do not forget to wite units for the final answer. 

•  Three charges $+q,-q$ and $Q$ are placed at the vertices of an equilateral triangle. Find the force and its direction on the charge $Q$.
•  Find the direction and magnitude of $\vec{E}$ at the center of a rhombus, with interior angles of $\pi/3$ and $2\pi/3$, with charges at the corners as shown in figure below. Assume that $ q= 1\times 10^{-8}$C, $a=5$cm 
• 1. [(a)]Show that the force on a charge at the center of an equilateral triangle due to a three equal charges placed at the vertices is zero.
  2. [(b)]What happens for a regular hexagon? a regular polygon with 2n sides?WHY?
• Twelve charges, $q_1,q_2,\ldots$ are placed on the consecutive corners of a regular polygon of 12 sides of length $a$. Find the resultant force on a charge $Q$ at the center if $q_1=2Q,q_5=2Q$ and all other charges are equal to $-3Q$.
• Two similar balls of mass $m$ are hung from silk threads of length $\ell$ and carry equal charges q. Assuming $\theta$ to be small show that the separation, $x$, between the balls is given by $$ x\approx \frac{q^2\ell}{2\pi\epsilon_0 mg} .$$ What is the value of $q$ if $\ell=120$cm, $m=10$g, $x=5$cm ?