A long straight wire carries a current $I$ along $y$-axis. The magnetic flux through a square placed a shown is $\frac{{\mu }_{0}I}{p\pi }ln\left(q\right)$. The $p\times q=$

A coil of area $10{ \mathrm{m}}^2$ is placed in a uniform magnetic field of $0.3 \mathrm{Wb} {\mathrm{m}}^{-2},$ with its plane perpendicular to the field. The coil rotates at a uniform rate to complete one revolution in $8 \mathrm{s}.$ Find the average $\mathrm{emf}$ in the coil during intervals when the coil rotates from

$\left(\mathrm{i}\right)0°$ to $90°$ 

(ii) $90°$ to $180°$ 

(iii) $180°$ to $270°$ 

(iv) $270°$ to $360°$

In a coil of resistance $50 \mathrm{\Omega }$, the induced current developed by changing magnetic flux through it, is shown in figure as a function of time. The magnitude of change in flux through the coil is

The magnetic flux linked with a coil, in where, is given by the equation $\varphi =3t^2+4t+9$.

Then, the magnitude of induced emf at $t=2 \mathrm{s}$ will be