Match List-I with List-II (the graphs of List-II are shown in the figure). The wires carry steady currents.
$$\begin{array}{|l|l|l|l|}\hline & \text{List-I (Y vs X)} & & \text{List-II (shape of graph)} \\ \hline \text{A.} & Y = \text{magnetic susceptibility},\ X = \text{magnetising field} & \text{I.} & \text{Graph I} \\ \hline \text{B.} & Y = \text{magnetic field},\ X = \text{distance from centre of a wire of radius } a \text{ for } x < a & \text{II.} & \text{Graph II} \\ \hline \text{C.} & Y = \text{magnetic field},\ X = \text{distance from centre of a wire of radius } a \text{ for } x > a & \text{III.} & \text{Graph III} \\ \hline \text{D.} & Y = \text{magnetic field inside a solenoid},\ X = \text{distance from centre} & \text{IV.} & \text{Graph IV} \\ \hline \end{array}$$
Choose the correct answer from the options given below:
Answer: (D) (A)-(III), (B)-(I), (C)-(IV), (D)-(II)
- (A) The susceptibility of a (para- or dia-magnetic) material does not depend on the field: horizontal line → III.
- (B) Inside a wire with uniform current, $B = \dfrac{\mu_0Ix}{2\pi a^2} \propto x$ → I.
- (C) Outside the wire, $B = \dfrac{\mu_0I}{2\pi x} \propto \dfrac1x$ → IV.
- (D) Inside a long solenoid the field is uniform and drops near the ends → II.
Solution by Sreeraj P, M.Sc Physics