Magnetic Field Due to a Current Element, Biot-Savart Law

Three infinitely long thin wires each carrying current $i$ in the same direction, are in the x-y plane a gravity-free space. The central wire is along the y-axis while the other two are along $x=\mp d$ Find the locus of the points for which the magnetic field B is zero.

A ring of the radius $R$ is placed in the $y-z$ plane and it carries a current $i$. The conducting wires which are used to supply the current to the ring can be assumed to be very long and are placed as shown in the figure. The magnitude of the magnetic field at the centre of the ring $\mathrm{A}$ is

Find the magnetic induction at point $O$, if the current carrying wire is in the shape shown in the figure.

Find the magnetic induction at the origin in the figure shown.

A system of long four parallel conductors whose sections with the plane of the drawing lie at the vertices of a square there flow four equal currents. The directions of these currents are as follows : those marked $\otimes$ point away from the reader, while those marked with a dot point towards the reader. How is the vector of magnetic induction directed at the centre of the square ?

A long straight wire carries a current of $10 \mathrm{A}$ directed along the negative $y-$axis as shown in the figure. A uniform magnetic field $B_0$ of magnitude ${10}^{-6} \mathrm{T}$ is directed parallel to the $x-$axis. What is the resultant magnetic field at the following point $\left(\mathrm{x}=2 \mathrm{m}, \mathrm{z}=0\right)$?
 

The magnetic field $d\overrightarrow{B}$ due to a small current element $\overrightarrow{d}$ at a distance $\overrightarrow{r}$ and element carrying current $i$ is.

A current of $i$ ampere is flowing in an equilateral triangle of side $a$. The magnetic induction at the centroid will be:

Which of the following equations correctly represents the relationship between permeability and permittivity of free space?

Which law is similar to the Biot-Savart's law of magnetism?

Calculate the magnitude of magnetic induction in air at a point $3 \mathrm{m}$ from one end of a $2 \mathrm{m}$ long current carrying wire and lying on its axis. A current of $1 \mathrm{A}$ is flowing through the wire. 

As indicated in the following figure a circular conducting wire is connected in such a way that current flows through two arcs of lengths $L_1$ and $L_2$ respectively. Calculate the magnitude of magnetic induction at the centre of the coil.

Find the intensity of magnetic field at a distance $r/2$ from a straight current carrying wire, if the intensity of magnetic field at a point situated at a distance $r$ from the same wire is $B$.

A long wire bent as shown in the figure carries current  $I=10 \mathrm{A}$. It is given that the radius of the semicircular portion is $1 \mathrm{m}$. What is the magnetic induction (in $\mathrm{\mu T}$) at the centre $c$ ?

A  current element of length $\mathrm{d}l$ and carrying current $I$ in $+z$ direction is placed at $(1,1,0)$. Let magnetic field at origin be ${\overrightarrow{B}}_1$ and at point $(2,2,0)$ be ${\overrightarrow{B}}_2$, then which of the following is correct?

A $V$ shaped wire lies in the $x-y$ plane. What is the direction of the magnetic field at $\mathrm{P}$ ?

What rule is used to find the direction of current induced in a wire moving in a magnetic field?

The magnetic induction at a point on the axis $\mathrm{O}$ due to five long current carrying wires $\mathrm{A}$, $\mathrm{B}$, $\mathrm{C}$, $\mathrm{D}$ and $\mathrm{E}$ which form the edges of a pentagonal prism as shown in figure is: ( The current in each wire is $\mathrm{I}$ and axis $\mathrm{O}$ is at a distance $\mathrm{R}$ from each wire) 

Find magnetic field at centre of loop, If wire of length $L$ form a loop of radius $R$ and have $n$ turn and current flowing in loop is $\mathrm{I}$ :-

A magnetic intensity of $1500 \mathrm{A} {\mathrm{m}}^{-1}$ produces a flux of $2.4\times {10}^{-5} \mathrm{Wb}$ in a iron bar of cross sectional area $0.5 {\mathrm{cm}}^2$. The permeability of the iron bar is