Biot-Savart’s Law

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.

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 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?

What is a current element ? Derive an expression for the magnetic filed due to a current element.

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

The magnetic field due to a current element is independent of _____ (nature of material/ current through it/ length of material).
 

What is the current element vector?

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 $O$.

The current in flowing along the path $ABCD$ of a cube (shown in the left figure) produces a magnetic field at the centre of cube of magnitude $B$. Dashed line depicts the non-conducting part of the cube.

Consider a cubical shape shown to the right which is identical in size and shape to the left. If the same current now flows in along the path $DAEFGCD$, then the magnitude of magnetic field at the centre 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?

Study the given current carrying configuration in the adjoining diagram and calculate the magnetic induction due to the same at a point $P$.

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.