The net magnetic flux through any closed surface is

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)

$A$ square of side $L$ meter lies in the $x-y$ plane in a region where the magnetic field is given by $\overrightarrow{B} = B_0(2 \hat{i} + 4 \hat{j} + 3 \hat{k}) \text{ T}$,where $B_0$ is a constant. The magnitude of the magnetic flux passing through the square is . . . . . . .

The dimensions of magnetic flux are

$A$ 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.

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: