Biot-Savart’s Law

Biot-savarts law does a common alteration of-

Infinite number of straight wires each carrying current I are equally placed as shown in the figure. Adjacent wires have current in opposite direction. Net magnetic field at point P is.

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.

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 long straight wire $AB$ carries a current $I$. A proton $P$ travels with a speed $v$, parallel to the wire, at a distance $d$ from it in a direction opposite to the current as shown in the figure. What is the force experienced by the proton and what is its direction?

The relative permeability of a medium is $0.075$. What is the magnetic susceptibility.

Magnetic field at a distance $r$ from an infinitely long straight conductor carrying a steady current varies as

The magnetic field due to current carrying a circular loop of radius $5 \mathrm{cm}$ at a point on the axis at a distance of $12 \mathrm{cm}$ from the center is $250 \mathrm{\mu T}.$ The magnetic field at the center of the loop is

A current $i$ carrying circular arc wire $AB$ of the length $L$ is turned along a circle, as shown in the figure. The magnetic field at the centre $O$.

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 $c$ ?

What is the magnetic field at centre $O$ of an equilateral triangle of side $2 \mathrm{cm}$ with current flowing as shown below? (Resistance of part ABC is $2 \mathrm{\Omega }$, and resistance of part ADC is $4 \mathrm{\Omega }$)

What is the magnetic field at point $P$ ?