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:

Write the dimensional formula for magnetic flux.

Consider a circular coil of wire carrying constant current $I$,forming a magnetic dipole. The magnetic flux through an infinite plane that contains the circular coil and excluding the circular coil area is given by $\phi_{i}$. The magnetic flux through the area of the circular coil area is given by $\phi_{0}$. Which of the following options is correct?

Assertion $(A)$: Magnetic flux is a vector quantity.
Reason $(R)$: Value of magnetic flux can be positive, negative, or zero.

Two circular loops of diameters $0.6 \,cm$ and $40 \,cm$ are kept coaxially with a separation of $15 \,cm$ between their centres. If a current $2 \,A$ flows through the smaller loop, then the flux linked with the bigger loop is (approximately)

$A$ circular disc of radius $0.2 \; m$ is placed in a uniform magnetic field of induction $\frac{1}{\pi} \; Wb/m^2$ in such a way that its axis makes an angle of $60^{\circ}$ with $\vec{B}$. The magnetic flux linked with the disc is..... $Wb$.