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

STATEMENT 1 : The sensitivity of a moving coil galvanometer is increased by placing a suitable magnetic material as a core inside the coil.

and

STATEMENT 2 : Soft iron has a high magnetic permeability and cannot be easily magnetized or demagnetized.

A magnetic field $$\overrightarrow{\mathrm{B}}=\mathrm{B}_{0} \hat{j}$$ exists in the region $$a < x < 2 a$$ and $$\overrightarrow{\mathrm{B}}=-\mathrm{B}_{0} \hat{j}$$, in the region $$2 a < x < 3 a$$, where $$\mathrm{B}_{0}$$ is a positive constant. A positive point charge moving with a velocity $$\vec{v}=v_{0} \hat{i}$$, where $$v_{0}$$ is a positive constant, enters the magnetic field at $$x=a$$. The trajectory of the charge in this region can be like,

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 and indicate your answer by darkening appropriate bubbles in the $$4 \times 4$$ matrix given in the ORS.

Column I | Column II | ||
---|---|---|---|

(A) | Point P is situated midway between the wires. |
(P) | The magnetic fields (B) at P due to the currents in the wire are in same direction. |

(B) | Point P is situated at the mid-point of the line joining the centers of the circular wires, which have same radii. |
(Q) | The magnetic fields (B) at P due to the currents in the wires are in opposite directions. |

(C) | Point P is situated at the mid-point of the line joining the centers of the circular wires, which have same radii. |
(R) | There is no magnetic field at P. |

(D) | Point P is situated at the common center of the wires. |
(S) | The wires repel each other. |