Magnetic flux cannot be zero at any instant.

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

A square loop of side $a$ lies in the $x-y$ plane with its sides parallel to the axes. It is moved into a region of magnetic field with a constant velocity $\overrightarrow{v}$ in the $x$-direction. The magnetic field in one region of width$a$ is given by $\overrightarrow{B}=B_0\hat{k}$ and in an adjacent region, also of width $a$, the magnetic field is $\overrightarrow{B}=-B_0\hat{k}$

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Which of the following graphs shows the emf induced in the loop as it enters the field region and finally leaves it? In these graphs $E_0=B_{0}av$.

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 $360°$

A coil is placed in magnetic field such that plane of coil is perpendicular to the direction of magnetic field. The magnetic flux through a coil can be changed:

A. By changing the magnitude of the magnetic field within the coil.

B. By changing the area of coil within the magnetic field.

C. By changing the angle between the direction of magnetic field and the plane of the coil.

D. By reversing the magnetic field direction abruptly without changing its magnitude.

Choose the most appropriate answer from the options given below:

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