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:

$A$ square of side $x \, m$ lies in the $x-y$ plane in a region where the magnetic field is given by $\vec B = B_0 (3\hat i + 4\hat j + 5\hat k ) \, T$,where $B_0$ is a constant. The magnitude of the magnetic flux passing through the square is:

$A$ square loop of side $1\,m$ and resistance $1\,\Omega$ is placed in a magnetic field of $0.5\,T$. If the plane of the loop is perpendicular to the direction of the magnetic field,the magnetic flux through the loop is $\dots\dots$ weber.

Verify Gauss's law for the magnetic field of a point dipole of dipole moment $\vec{m}$ at the origin for a surface which is a sphere of radius $R$.

$A$ flux of $1 \ mWb$ passes through a strip having an area $A = 0.02 \ m^2$. The plane of the strip is at an angle of $60^{\circ}$ to the direction of a uniform field $B$. The value of $B$ is

The unit of magnetic flux is