A conductor of length 1.5 m and area of cross-section $3 \times 10^{-5} \mathrm{~m}^2$ has electrical resistance of $15 \Omega$.

The current density in the conductor for an electric field of $21 \mathrm{Vm}^{-1}$ is

The relation between the current $i$ (in ampere) in a conductor and the time $t$ (in second) is $i=12 t+9 t^2$. The charge passing through the conductor between the times $t=2 \mathrm{~s}$ and $t=10 \mathrm{~s}$ is

A long straight rod of diameter 4 mm carries a steady current $i$. The current is uniformly distributed across its cross-section. The ratio of the magnetic fields at distances 1 mm and 4 mm from the axis of the rod is

A straight wire of length 20 cm carrying a current of $\frac{3 .}{\pi^2} \mathrm{~A}$ is bent in the form of a circle. The magnetic field at the centre of the circle is