Ampere's Circuital Law

Current I is following along the path ABCD, along the four edges of the cube (figure-a) creates a magnetic field in the centre of the cube of ${\text{B}}_0$. Find the magnetic field B created at the centre of the cube current I following along the path of the six edges ABCDHEA figure - b

Two long conductors are arranged as shown above to form overlapping cylinders, each of radius r, whose centres are separated by a distance d. Current of density J flows into the plane of the page along the shaded part of one conductor and an equal current flows out of the plane of the page along the shaded portion of the other, as shown. What are the magnitude and direction of the magnetic field at point A ?

A cylindrical conductor of radius $R$ carries a current along its length. The current density $J$, however, is not uniform over the cross-section of the conductor but is a function of the radius according to $J=br$, where $b$ is a constant. Then the expression for the magnetic field



$\left(B_1\right)$ at $r_1<R$ and
$\left(B_{\mathrm{2}}\right)$ at distance $r_2>R$, measured from the axis is:

Six wires of current ${\mathrm{I}}_1=\mathrm{1 }\mathrm{A},{\mathrm{I}}_2=\mathrm{2 }\mathrm{A},{\mathrm{I}}_3=\mathrm{3 }\mathrm{A},{\mathrm{I}}_4=\mathrm{1 }\mathrm{A},{\mathrm{I}}_5=\mathrm{5 }\mathrm{A}$ and ${\mathrm{I}}_6=\mathrm{4 }\mathrm{A}$ cut the page perpendicularly at the points $\mathrm{1,\; 2,\; 3,\; 4,\; 5}$ and $6$ respectively as shown in the figure. Find the value of integral $\oint \overrightarrow{B}.d\overrightarrow{l}$ around the circular path $\mathrm{C.}$

What is similarity between gauss law and ampere's law?

Ampere's law is analogous to _____ law in electrostatics.

Ampere's law is analogous to

An infinite straight wire is passing through the centre of a circular loop of radius $R$. The wire carries a current $i$. The length of the wire makes an angle ${60}^0$ with the plane of the loop. The value is found $\int \vec{\mathrm{B}}\text{.d}\vec{\mathrm{l}}=\frac{\sqrt{x}}{2}{\mu }_{0}i$, when evaluated along the loop. Calculate the value of $x$.

A long straight wire of radius $a$ carries a steady current $i.$ The current is uniformly distributed across its cross-section. The ratio of the magnetic field at $\frac{a}{2}\mathrm{ }\mathrm{a}\mathrm{n}\mathrm{d} 2a$ is

When the number of turns in a toroidal coil is doubled, then the value of magnetic flux density will become,

The direction of a magnetic field at a point is given by the tangent to the magnetic lines of force at that point.

Defined magnetic field lines?

The magnetic field lines can intersect each other.

Explain the properties of magnetic field lines?

Properties of magnetic lines of force are:

Magnetic line of forces

Find the magnetic field created by a current carrying wire of current $2 \mathrm{A}$ at a distance of $10 \mathrm{cm}$ from the wire in micro Telsa.

The circular integral of magnetic field in a closed loop is proportional to the net current going through the area of the loop.

Choose the incorrect option-

The two ends of $\mathrm{a}$ non-conducting spring of force constant $50{\mathrm{Nm}}^{-1}$ and unstretched length of $2 \mathrm{cm}$ are connected to the mid points of two straight parallel rods each of length $4 \mathrm{m}$. When $100 \mathrm{A}$ current is passed through each rod in the same direction, the work done on the spring in $\mathrm{mJ}$ is