[2008EM/HMW-10]

IMSc-IV Physics-IV : Electricity and Magnetism Jan-Apr 2008 MM : 20 Set-X : Tutorial-VI Magnetic Flux, Induction

1. In Figure 1 below the magnetic flux through the loop perpendicular to the plane of coil and directed into the paper is varying according to the relation $$ \Phi_B =6 t^2 + 7t + 1 $$ where $\Phi_b$ is in milliwebers (1 milliweber=$10^{-3}$ weber) and $t$ is in seconds.
   1. What is the magnitude of the emf induced in the loop when $t=2$ sec ?
   2. What is the direction of current through $R$.
2. In Figure2 below shows a rectangular loop of resistance $R$, width $\ell$ and length $a$ being pulled at constant speed $v$ through a region of width $d$ in which a uniform field is setup by a magnet.
   1. Plot the flux of $B$ through the loop as function of the coil position $x$.
   2. Plot induced emf.
   3. Plot the rate of Joule heating in the loop.
3. A copper rod of length $L$ rotates at angular frequency $\omega$ in a uniform magnetic field $\vec{B}$ as shown in \Figref{em-cdr-0028}. Find emf developed between the two ends of the rod.\par