Choose the correct sketch of the magnetic field lines for a pair of parallel current-carrying wires,one with current flowing into the plane (represented by $\otimes$) and one with current flowing out of the plane (represented by $\odot$).

$A$ circular coil connected to a battery of emf $E$ produces a certain magnetic induction field at its centre. The coil is unwound,stretched to double its length,rewound into a coil of $1/3$ of the original radius,and connected to a battery of emf $E^{\prime}$ to produce the same field at the centre. Then $E^{\prime}$ is

One of the two small circular coils (neither having any self-inductance) is suspended with a $V$-shaped copper wire,with its plane horizontal. The other coil is placed just below the first one with its plane horizontal. Both coils are connected in series with a $dc$ supply. The coils are found to attract each other with a force. Which one of the following statements is incorrect?

The current flowing along the path $A B C D$ of a cube (shown in the left figure) produces a magnetic field at the centre of the cube of magnitude $B$. Dashed lines depict the non-conducting part of the cube. Consider a cubical shape shown to the right which is identical in size and shape to the left. If the same current now flows in along the path $D A E F G C D$,then the magnitude of the magnetic field at the centre will be

$A$ conductor lies parallel to the $Z$-axis between $-1.5 \le Z < 1.5 \text{ m}$,carrying a constant current of $10.0 \text{ A}$ in the $-\hat{a}_z$ direction. For the given magnetic field $\vec{B} = 3.0 \times 10^{-4} e^{-0.2x} \hat{a}_y \text{ T}$,find the power required to move the conductor at a constant speed from $x = 0$ to $x = 2.0 \text{ m}$ in a time interval of $5 \times 10^{-3} \text{ s}$. Assume the motion is parallel to the $X$-axis. ........... $\text{W}$

Match List-$I$ with List-$II$.

List-$I$	List-$II$
$(A)$ Permeability of free space	$(I) \ [M L^2 T^{-2}]$
$(B)$ Magnetic field	$(II) \ [M T^{-2} A^{-1}]$
$(C)$ Magnetic moment	$(III) \ [M L T^{-2} A^{-2}]$
$(D)$ Torsional constant	$(IV) \ [L^2 A]$

Choose the correct answer from the options given below: