A long insulated copper wire is closely wound as a spiral of N turns. The spiral has inner radius a and outer radius b. The spiral lies in the xy-plane and a steady current I flows through the wire. The z-component of the magnetic field at the centre of the spiral is

A thin flexible wire of length L is connected to two adjacent fixed points and carries a current I in the clockwise direction, as shown in the figure. When the system is put in a uniform magnetic field of strength B going into the plane of the paper, the wire takes the shape of a circle. The tension in the wire is

Electrical resistance of certain materials, known as superconductors, changes abruptly from a non-zero value to zero as their temperature is lowered below a critical temperature T_c(0). An interesting property of superconductors is that their critical temperature becomes smaller than T_c(0), if they are placed in a magnetic field, that is, the critical temperature T_c(B) is a function of the magnetic field strength B. The dependence of T_c(B) on B is shown in the figure.

In the graph below, the resistance R of a superconductor is shown as a friction of its temperature T for two different magnetic fields B₁ (solid line) and B₂ (dashed line). If B₂ is larger than B₁ which of the following graphs shows the correct variation of R with T in these fields?

Electrical resistance of certain materials, known as superconductors, changes abruptly from a non-zero value to zero as their temperature is lowered below a critical temperature T_c(0). An interesting property of superconductors is that their critical temperature becomes smaller than T_c(0), if they are placed in a magnetic field, that is, the critical temperature T_c(B) is a function of the magnetic field strength B. The dependence of T_c(B) on B is shown in the figure.

A superconductor has T_c(0) = 100 K. When a magnetic field of 7.5 T is applied, its T_c decreases to 75 K. For this material, one can definitely say that when