Biot-Savart Law

What is the importance of a radial magnetic field and how is it produced?

Explain how Biot-Savart law enables one to express the Ampere's circuital law in the integral form, viz., $\oint \overrightarrow{B}.\overrightarrow{dl}={\mu }_{0}I$, where $I$ is the total current passing through the surface.

Write, using Biot-Savart law, the expression for the magnetic field element $\overrightarrow{dl}$ carrying current $I$ at a distance $\overrightarrow{r}$ from it in a vector form.

Hence derive the expression for the magnetic field due to a current-carrying loop of radius $R$ at a point $P$  distant $x$ from its centre along the axis of the loop.

Use Biot-Savart law to derive the expression for the magnetic field due to a circular coil of radius $R$ having $N$ turns at a point on the axis at a distance $\text{'}x\text{'}$ from its centre. How is the direction of the magnetic field determined at this point? Draw the magnetic field lines due to this coil.

State Biot-Savart law expressing it in vector form. Use it to obtain the magnetic field, at an axial point, distant r from the centre of a circular coil of radius a carrying a current $I$. Hence, compare the magnitudes of the magnetic field of this coil at the centre and at an axial point for which $r=\sqrt{3}a$.

Use Biot-Savart's law to find the expression for the magnetic field due to a circular loop of radius $\text{'}r\text{'}$ carrying current $\text{'}I\text{'}$, at its centre.

Write any two important points of similarities and differences each between Coulomb's law for the electrostatic field and Biot-Savart's law for the magnetic field.

Show that the kinetic energy of the particle moving in a magnetic field remains constant.

Using Biot-Savart law, obtain the expression for the magnetic field due to a circular coil of radius $r$, carrying a current $I$ at a point on its axis distant $x$ from the centre of the coil.

State Biot-Savart law and express it in the vector form.

Using Biot-Savart's law, derive the expression for the magnitude of the magnetic field at the centre of a circular loop of radius $r$ carrying a steady current $I$. Draw the field lines due to the current loop.

A wire of length $L$ is bent into a semi-circular loop. Use Biot-Savart law to deduce an expression for the magnetic field at the centre due to current $I$ passing through it.

State Biot-Savart's law in vector form expressing the magnetic field due to an element $\overrightarrow{dl}$ carrying current $I$ at a distance $\overrightarrow{r}$ from the element. How will you find the direction of the magnetic field?

A square coil, $OPQR$, of side a, carrying a current $I$, is placed in the $Y-Z$ plane as shown in figure. Find the magnetic moment associated with this coil.

What is the nature of the magnetic field associated with the current in a straight conductor?

Show the magnetic lines of force around a straight current carrying conductor.

Write an expression for the magnetic field produced by an infinitely long straight wire carrying a current $I$ at a short distance $a$ from itself.

State the rule that is used to find the direction of magnetic field acting at a point near a current carrying straight conductor.

What is the value of $4\pi /{\mu }_0$?

What is the SI unit of ${\mu }_0$?