$A$ long straight wire carries a current of $35\, A$. What is the magnitude of the magnetic field $B$ at a point $20\, cm$ from the wire?

Six very long insulated copper wires are bound together to form a cable. The currents carried by the wires are $I_1 = +10 \text{ A}, I_2 = -13 \text{ A}, I_3 = +10 \text{ A}, I_4 = +7 \text{ A}, I_5 = -12 \text{ A}$ and $I_6 = +18 \text{ A}$. The magnetic induction at a perpendicular distance of $10 \text{ cm}$ from the cable is (Given: $\mu_0 = 4\pi \times 10^{-7} \text{ T m/A}$) (in $\mu\text{T}$)

Which convention is used to represent currents and magnetic fields emerging out of a surface?

Two concentric coils $X$ and $Y$ of radii $16 \, cm$ and $10 \, cm$ lie in the same vertical plane containing $N-S$ direction. Coil $X$ has $20$ turns and carries $16 \, A$. Coil $Y$ has $25$ turns and carries $18 \, A$. Coil $X$ has current in anticlockwise direction and coil $Y$ has current in clockwise direction for an observer looking at the coils facing the west. The magnitude of the net magnetic field at their common centre is:

Two similar coils each of radius $R$ are lying concentrically with their planes at right angles to each other. The currents flowing in them are $I$ and $2I$. The resultant magnetic field of induction at the centre will be ($\mu_0 =$ Permeability of vacuum).

$A$ small cube of side $1 \text{ mm}$ is placed at the centre of a circular loop of radius $10 \text{ cm}$ carrying a current of $2 \text{ A}$. The magnetic energy stored inside the cube is $\alpha \times 10^{-14} \text{ J}$. The value of $\alpha$ is . . . . . . . ($\mu_0 = 4\pi \times 10^{-7} \text{ Tm/A}$, $\pi = 3.14$)