The magnetic field at the centre of a current-carrying circular coil is

Two long straight parallel conductors carry currents $I_1$ and $I_2$ $(I_1 > I_2)$. When the direction of $I_1$ and $I_2$ is the same,the magnetic field intensity midway between the two conductors is $20 \mu T$. If the direction of $I_2$ is reversed,the field intensity becomes $50 \mu T$. The ratio $I_2 / I_1$ is:

In a hydrogen atom,an electron moves in a circular orbit of radius $5.2 \times 10^{-11} \, m$ and produces a magnetic induction of $12.56 \, T$ at its nucleus. The current produced by the motion of the electron will be (Given $\mu_0 = 4\pi \times 10^{-7} \, Wb/A \cdot m$)

$A$ current carrying circular loop of radius '$R$' and a current carrying long straight wire are placed in the same plane. $I_c$ and $I_w$ are the currents through the circular loop and the long straight wire,respectively. The perpendicular distance between the centre of the circular loop and the wire is '$d$'. The magnetic field at the centre of the loop will be zero when the separation '$d$' is equal to:

Two concentric circular coils $A$ and $B$ have radii $20 \text{ cm}$ and $10 \text{ cm}$ respectively and lie in the same plane. The current in coil $A$ is $0.5 \text{ A}$ in the anticlockwise direction. What is the current in coil $B$ such that the net magnetic field at the common centre is zero?

$A$ battery is connected between two points $A$ and $B$ on the circumference of a uniform conducting ring of radius $r$ and resistance $R$. One of the arcs $AB$ of the ring subtends an angle $\theta$ at the centre. The value of the magnetic induction at the centre due to the current in the ring is