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

$N$ equally spaced charges,each of value $q$,are placed on a circle of radius $R$. The circle rotates about its axis with an angular velocity $\omega$ as shown in the figure. $A$ bigger Amperian loop $B$ encloses the whole circle,whereas a smaller Amperian loop $A$ encloses a small segment. The difference between enclosed currents,$I_A - I_B$,for the given Amperian loops is

$A$ long curved conductor carries a current $I$. $A$ small current element of length $dl$ on the wire induces a magnetic field at a point away from the current element. If the position vector between the current element and the point is $\vec{r}$,making an angle $\theta$ with the current element,then the induced magnetic field density $d\vec{B}$ at the point is $(\mu_0 = \text{permeability of free space})$:

The magnitude of the force per unit length acting on a thin wire carrying a current $I=8 \text{ A}$ at a point $O$,if the wire is bent as shown in the figure with a radius $R=10 \pi \text{ cm}$,is (in $\mu \text{N/m}$)

The Earth's magnetic field at a given point is $0.5 \times 10^{-5} \, Wb/m^2$. This field is to be annulled by the magnetic induction at the center of a circular conducting loop of radius $5.0 \, cm$. The current required to be flown in the loop is nearly......$A$

If a wire of length $L$ forms a loop of radius $R$ and has $n$ turns,find the magnetic field at the center of the loop if the current flowing in the loop is $I$.