[2008EM/HMW-08]

IMSc-IV Physics-IV : Electricity and Magnetism Jan-Apr 2008 MM : 20 Set-IX : Group Activity-IV Gauss Law, Conductors

• Two infinite long wires, carrying currents $I$ and $2I$, pass through points $A,B$ separated by a distance $10L$, as shown in figure below.
  • Sketch a figure to show the directions of the magnetic field due the two wires at a point $P$ at distance $12L$ from the line $AB$.
  • Find the magnitude and direction of the resultant magnetic field due to the two wires at point $P$.
  
• Find the magnetic field at a point $P$ for each of the steady state current configurations shown below. 
• A long straight wire carrying a current $3I$ is placed in the plane having a rectanglar loop carrying current $2I$ as shown in the figure.
  • What are the magnitude and directions of magnetic force on the loop the two sides $AD$ and $BC$ due to the current in the straight wire?
  • Divide the side $AB$ into small line elements, write the force on a small line element and hence find the net magnetic force on the side $AB$ due the straight wire.
  • Compute the net force on the loop when $I=10$A, $L=10$ cm, $a=1$cm, $b=80$cm.
  
• Find the magnetic field at the center of a $n$ sided regular polygon carrying a steady current $I$. Show that as $n$ tend goes infinity, the expression for the magnetic field goes over to that of the magnetic field due to a circular loop.