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

Biot-savarts law does a common alteration of-

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 $\left(\mathrm{x}=2 \mathrm{m}, \mathrm{z}=0\right)$?
 

A current $I$ is flowing through the sides of an equilateral triangle of side $a$. The magnitude of the magnetic field at the centroid of the triangle is

What are the directions of the magnetic field between and outside a pair of two parallel large sheets carrying currents in the same directions, as illustrated in Figure (from the side shown)?

A current of $5 \mathrm{A}$ is flowing from south to north in a straight wire. Find the magnetic field due to $1 \mathrm{cm}$ piece of wire at a point $1 \mathrm{m}$ North-East from the piece of wire.

The current flows from $A$ to $B$ as shown in the figure. The direction of the induced current in the loop is:

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:

What is the unit of ${\mu }_{\circ }$?

Find the magnetic induction at point $O$ if the wire carrying a current $I$ has the shape shown in figure.

A long coaxial cable consists of two thin-walled conducting cylinders with inner cylinder radius $2 \mathrm{cm}$ and outer cylinder radius $8 \mathrm{cm}$. The inner cylinder carries a steady current $0.1 \mathrm{A}$, and the outer cylinder provides the return path for that current. The current produces a magnetic field between the two cylinders. Find the energy stored in the magnetic field for length $5 \mathrm{m}$ of the cable. Express answer in $\mathrm{nJ}$ (use $\ln 2=0.693$ )

A long straight wire, carrying a current $I$ is bent at its mid point to form an angle of $60°$. At a point $P$ distance $R$ from the point of bending the magnetic field is

Permeability of free space is also known as _____.

Explain Biot-Savart law.

How do you find the permeability of a medium?