In a Thomson mass spectrograph,the electric field and magnetic field are applied:

The temperature at which the thermo-electric power of a thermocouple becomes zero is called:

$A$ current is flowing through a thin cylindrical shell of radius $R$. If the energy density in the medium,due to the magnetic field,at a distance $r$ from the axis of the shell is equal to $U$,then which of the following graphs is correct?

Two wires each carrying a steady current $I$ are shown in four configurations in Column $I$. Some of the resulting effects are described in Column $II$. Match the statements in Column $I$ with the statements in Column $II$.

Column $I$	Column $II$
$(A)$ Two parallel wires with current in the same direction,$P$ is the midpoint.	$(p)$ The magnetic fields $(B)$ at $P$ due to the currents in the wires are in the same direction.
$(B)$ Two coaxial circular loops with current in the same direction,$P$ is the midpoint on the axis.	$(q)$ The magnetic fields $(B)$ at $P$ due to the currents in the wires are in opposite directions.
$(C)$ Two coplanar circular loops with current in opposite directions,$P$ is the midpoint.	$(r)$ There is no magnetic field at $P$.
$(D)$ Two concentric coplanar circular loops with current in the same direction,$P$ is the common center.	$(s)$ The wires repel each other.

Two circular coils $1$ and $2$ are made from the same wire,but the radius of the first coil is twice that of the second coil. What is the ratio of the potential difference applied across them so that the magnetic field at their centres is the same?

$A$ long thin-walled pipe of radius $R$ carries a current $I$ along its length. The current density is uniform over the circumference of the pipe. The magnetic field at the center of the pipe due to the quarter portion of the pipe shown is: