Biot-Savart 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.

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?

Define the relative permittivity of a medium.

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

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

An electron moving in a circular orbit of radius $R$ makes $n$ revolution per second. What is the magnitude of the magnetic field strength at the centre ?

An elevator carrying a charge of $0.5$ $\mathrm{C}$ is moving down with a velocity of $5\times {10}^3 \mathrm{m} {\mathrm{s}}^{-1}$. The elevator is $4 \mathrm{m}$ from the bottom and $3 \mathrm{m}$ horizontally from $P$ as shown in the figure. What magnetic field in $\left( \mathrm{\mu }\mathrm{T}\right)$ does it produce at point $P$.

A square loop of side $a=6$ $\mathrm{cm}$ carries a current $I=1 \mathrm{A}$. Calculate magnetic induction $B (\mathrm{i}\mathrm{n} \mathrm{\mu }\mathrm{T})$ at point $P$, lying on the axis of loop and at a distance $x=\sqrt{7}$ $\mathrm{cm}$ from the center of loop.

A long straight wire in the horizontal plane carries a current of 75 A in north to south direction, magnitude and direction of field B at a point 3 m east of the wire is

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

If magnetic field at point $P$ is ${10}^{-4}$ Tesla. Determine current $\prime i\prime$ ?

In the given figure, what is the magnetic field induction at point $O$ .

Current $I$ is flowing along the path ABCD, along the four edges of the cube (figure-a), creates a magnetic field in the centre of the cube of $B_0$ . Find the magnetic field B created at the centre of the cube by a current $I$ flowing along the path of the six edges ABCGHEA (figure-b)

A square loop is made by a uniform conductor wire as shown in figure


The net magnetic field at the centre of the loop if side length of the square is a