$A$ circular coil $A$ has a radius $R$ and the current flowing through it is $I$. Another circular coil $B$ has a radius $2R$ and the current flowing through it is $2I$. The ratio of the magnetic fields at the centre of the circular coils $(B_A : B_B)$ is: (in $:1$)

$A$ circular loop of a wire and a long straight wire carry currents $I_c$ and $I_e$,respectively,as shown in the figure. Assuming that these are placed in the same plane,the magnetic field will be zero at the centre of the loop when the separation $H$ is:

What should be the current $i$ (in $A$) in a circular coil of radius $5\,cm$ to annul the horizontal component of Earth's magnetic field ${B_H} = 5 \times {10^{ - 5}}\,T$?

The magnetic field at the point of intersection of diagonals of a square wire loop of side $L$ carrying a current $I$ is

In the following figure,the magnitude of the magnetic field at the point $P$ is:

Two long parallel wires are separated by a distance of $2.50 \ cm$. The force per unit length that each wire exerts on the other is $4 \times 10^{-5} \ N \ m^{-1}$,and the wires repel each other. The current in one wire is $0.5 \ A$. What is the current in the second wire (in $A$)? (Take $\mu_0 = 4 \pi \times 10^{-7} \ S.I. \ \text{unit}$)