An arc of a circle of radius $R$ subtends an angle $\frac{\pi}{2}$ at the centre. It carries a current $I$. The magnetic field at the centre will be ($\mu_0 =$ permeability of free space).

$A$ wire of length $l$ is bent into a circular coil of one turn of radius $R_1$. Another wire of the same material and same area of cross-section and same length is bent into a circular coil of two turns of radius $R_2$. When the same current flows through the two coils, the ratio of magnetic induction at the centres of the two coils is

$A$ particle having a charge $100 e$ is revolving in a circular path of radius $0.8 \ m$ with $1 \ r.p.s$. The magnetic field produced at the center of the circle in $SI$ unit is ($\mu_0$ is the permeability of vacuum,$e = 1.6 \times 10^{-19} \ C$).

Two long straight conductors with currents $I_1$ and $I_2$ are placed along $X$ and $Y$-axes respectively. The equation of the locus of points of zero magnetic induction is:

Two infinitely long wires, each carrying a current $I = 10 \ A$, are bent to form a right angle as shown in the figure. Find the magnetic induction at point $O$. $\left[\mu_0 = 4\pi \times 10^{-7} \ H \ m^{-1}\right]$

$A$ horizontal overhead powerline is at a height of $5 \,m$ from the ground and carries a current of $150 \,A$ from East to West. The magnetic field directly below it on the ground is