A wire carrying current $i$ is shaped as shown. Section $AB$ is a quarter circle of radius $r$. The magnetic field is directed
At an angle $\pi /4$ to the plane of the paper
Perpendicular to the plane of the paper and directed in to the paper
Along the bisector of the angle $ACB$ towards $AB$
Along the bisector of the angle $ACB$ away from $AB$
A current of $10\,A$ is passing through a long wire which has semicircular loop of the radius $20\,cm$ as shown in the figure. Magnetic field produced at the centre of the loop is
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 if $2I$ is the current flowing through it, then the magnetic fields at the centre of the circular coil are in the ratio of (i.e.${B_A}$ to ${B_B}$)
The magnetic field at the centre of a wire loop formed by two semicircular wires of radii $R_1=2 \pi\ \mathrm{m}$ and $R_2=4 \pi\ \mathrm{m}$ carrying current $I=4 \mathrm{~A}$ as per figure given below is $\alpha \times 10^{-7} \mathrm{~T}$. The value of $\alpha$ is___________ (Centre $\mathrm{O}$ is common for all segments)
A particle is moving with velocity $\overrightarrow{ v }=\hat{ i }+3 \hat{ j }$ and it produces an electric field at a point given by $\overrightarrow{ E }=2 \hat{ k }$. It will produce magnetic field at that point equal to (all quantities are in SI units)
Two concentric circular coils $X$ and $Y$ of radii $16\; cm$ and $10\;cm$ respectively, lie in the same vertical plane containing the north to south direction. Coil $X$ has $20$ turns and carries a current of $16\; A$ coil $Y$ has $25$ turns and carries a current of $18\; A$. The sense of the current in $X$ is anticlockwise, and clockwise in $Y$, for an observer looking at the coils facing west. Give the magnitude and direction of the net magnetic field due to the coils at their centre.