### Electromagnetic Induction

goals
Write the dimensions of Magnetic flux in terms of mass, time, length and charge.
Some magnetic flux is changed in a coil of resistance $10$ ohm. As a result an induced current is developed in it, which varies with time as shown in figure. The magnitude of change in flux through the coil in Webers is (Neglect self inductance of the coil)
A coil has an area of $0.05{m}^{2}$ and it has $800$ turns. It is placed perpendicular in a magnetic field of strength $4\times {10}^{-5}Wb/{m}^{2}$, it is rotated through ${90}^{o}$ in $0.1sec$. The average emf induced in the coil is
A uniform field of induction $B$ is changing in magnitude at a constant rate $dB/dt$. You are given a mass $m$ of copper which is to be drawn into a wire of radius $r$ and formed into a circular loop of radius $R$. Show that the induced current in the loop does not depend on the size of the wire of the loop. Assuming $B$ perpendicular the loop prove that the induced current $i=\dfrac { m }{ 4\pi \rho \delta } \dfrac { dB }{ dt }$ where $\rho$, is the resistivity and $d$ is the density of copper.

Electric charge is uniformly distributed along a long straight wire of a radius of 1 mm. The Charge per cm length of the wire is Q coulomb. Another cylindrical surface of radius 50 cm and length 1 m symmetrically encloses the wire as shown in fig. The total flux passing through the cylindrical surface is: