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?

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

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

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

A current of 1 A is flowing along the sides of an equilateral triangle of side $4.5\times {10}^{-2}$ . The magnetic field at the centroid of the triangle is $\left({\mu }_0=4\pi \times {10}^{-7}H/m\right)$

When current is passed through a circular wire prepared from a long conducting wire, the magnetic field produced at its centre is B. Now a loop having two turns is prepared from the same wire and the same current is passed through it. The magnetic field at its centre will be ..............

Two observers moving with different velocities see that a point charge produces same magnetic field at the same point $A$. Their relative velocity must be parallel to $\overrightarrow{r},$ where $\overrightarrow{r}$ is the position vector of point $A$ with respect to point charge. This statement is

The magnetic induction at a point $P$ which is at a distance of $4 \mathrm{cm}$ from a long current carrying wire is ${10}^{-3} \mathrm{T}$ . The field of induction at a distance $12 \mathrm{cm}$ from the current will be

A current is flowing north along a power line. The direction of the magnetic field above it, neglecting the earth's field, is towards,

Which of the following graphs, shows the variation of magnetic induction B with distance r from a long wire carrying a current

A pair of stationary and infinitely long bent wires are placed in the x-y plane as shown in figure. The wires carry a current I = 10A each as shown. The segments L and M are along X- axis. the segments P and Q are along the Y- axis such that OS =OR= 0.02m. The magnitude and direction of the magnetic induction at origin O is

Two long concentric cylindrical conductors of radii $\mathrm{a}$ & $\mathrm{b}\left(\mathrm{b}<\mathrm{a}\right)$ are maintained at a potential difference $\mathrm{V}$ & carry equal & opposite currents $\mathrm{I}$ . An electron with a particular velocity $\mathrm{\prime }\mathrm{\prime }\mathrm{U}\mathrm{\prime }\mathrm{\prime }$ parallel to the axis will travel undeviated in the evacuated region between the conductors. Then $\mathrm{U}=$

The negatively and uniformly charged non-conducting disc, as shown, is rotated clockwise. The direction of the magnetic field at point $A$ in the plane of the disc is,

        

Magnetic field through the loop varies with  time 't' as shown in the figure. (Positive magnetic field implies magnetic field perpendicular to the plane of the loop and assume anticlockwise current as positive). Choose correct graph for induced current  I in the loop