The magnetic flux linked with a closed coil is increased to a maximum value in $2 \,s$ and its relation with time is $\phi = at^2 + bt + c$. Then the relation between $a, b$ and $c$ is:

Assertion $(A)$: When the plane of the coil is perpendicular to the magnetic field,the magnetic flux linked with the coil is minimum,but the induced emf is zero.
Reason $(R)$: $\phi = nAB \cos \theta$ and $e = -\frac{d\phi}{dt}$.

The unit of magnetic flux is

What is the difference between Gauss's law in electrostatics and Gauss's law in magnetism?

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

$A$ long straight wire carrying a constant current $i$ is placed in the same plane as a rectangular loop of length $l$. The distance of the sides of the loop from the wire are $r_1$ and $r_2$. If the area under the curve of the magnetic field $B$ versus distance $r$ graph between $r_1$ and $r_2$ is $A$,find the magnetic flux through the loop.