What is the ratio of the magnetic field at the center of a circular ring of radius $R$ to the magnetic field at a point on its axis at a distance of $3R$ from the center?

Which one of the following options represents the magnetic field $\vec{B}$ at $O$ due to the current $I$ flowing in the given wire segments lying on the $xy$ plane?

$A$ uniform circular wire loop is connected to the terminals of a battery. The magnetic field induction at the centre due to $ABC$ portion of the wire will be (length of $ABC = l_1$, length of $ADC = l_2$):

Two identical wires $A$ and $B$,each of length $l$,carry the same current $I$. Wire $A$ is bent into a circle of radius $R$ and wire $B$ is bent to form a square of side $a$. If $B_A$ and $B_B$ are the values of magnetic field at the centres of the circle and square respectively,then the ratio $\frac{B_A}{B_B}$ is

As shown in the figure,two infinitely long,identical wires are bent by $90^{\circ}$ and placed in such a way that the segments $LP$ and $QM$ are along the $x-$ axis,while segments $PS$ and $QN$ are parallel to the $y-$ axis. If $OP = OQ = 4\, cm$,the magnitude of the magnetic field at $O$ is $10^{-4}\, T$,and the two wires carry equal current $i$ (see figure),find the magnitude of the current in each wire and the direction of the magnetic field at $O$. $(\mu_0 = 4\pi \times 10^{-7}\, NA^{-2})$

$A$ current of $1 \,A$ is flowing along the sides of an equilateral triangle of side $a = 4.5 \times 10^{-2} \,m$. The magnetic field at the centroid of the triangle is $(\mu_0 = 4 \pi \times 10^{-7} \,T \cdot m/A)$.