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.

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

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 permeability is defined as the ratio of Magnetic induction and magnetising field

What is difference between permeability and permittivity of medium?

Both Biot-savarts law and Coulomb's law works on the principle of Superposition.

Write any two differences between Coulomb's law for the electrostatic field and Biot-Savart's for the magnetic Field.

How is the speed of light related to the permittivity and permeability of free space?

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

What is the relation between permeability and permittivity of free space?

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

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 $\prime i\prime$ ?

The direction of magnetic field $\overrightarrow{dB}$ due to current element $\overrightarrow{dl}$ at a distance r is the direction of