A very long wire $ABDMNDC$ is shown in figure carrying current $I. AB$ and $BC$ parts are straight, long and at right angle. At $D$ wire forms a circular turn $DMND$ of radius $R. AB.$ $\mathrm{BC}$ parts are tangential to circular turn at $\mathrm{N}$ and $D$. Magnetic field at the centre of circle is

If wire of length $L$ form a loop of radius $R$ and have $n$ turn. Find magnetic field at centre of loop if current flowing in loop is $I$

In a region of space, a uniform magnetic field $B$ exists in the $y-$direction.Aproton is fired from the origin, with its initial velocity $v$ making a small angle $\alpha$ with the $y-$ direction in the $yz$ plane. In the subsequent motion of the proton,

Consider two thin identical conducting wires covered with very thin insulating material. One of the wires is bent into a loop and produces magnetic field $B_1,$ at its centre when a current $I$ passes through it.The second wire is bent into a coil with  three identical loops adjacent to each other and produces magnetic field $B_2$ at the centre of the loops when current $I/3$ passes through it. The ratio $B_1 : B_2$ is

Magnetic field at the centre $O$ of a square loop of side $'a'$ carrying current $I$ as shown in the figure is

In the following figure a wire bent in the form of a regular polygon of $n$ sides is inscribed in a circle of radius $a$. Net magnetic field at centre will be