# Biot Savart Law: Meaning & Applications (2023)

Did you wonder why electricity is essential for loudspeakers to work? We all have used loudspeakers during parties and other different occasions. However, there is mostly a moment when the light goes off, and there is silence as the loudspeakers cannot work. Sometimes, we were in the middle of our favorite song, or our favorite song was about to begin. Pretty long wait for electricity, right? Fig. 1 - The figure shows a loudspeaker membrane that vibrates during sound generation.

Well, electricity is essential for the generation of sound from loudspeakers. A changing electric current is passed through the coil inside the loudspeaker to generate a magnetic field. This coil is passed through magnets placed inside the speaker. The magnetic field generated by the coil is opposite to the direction of a magnetic field due to these magnets. This opposing magnetic field causes the membrane's vibration, producing sound. A well-known law in physics that helps to understand this magnetic field generated due to the passing of an electric current through the coil is the Biot-Savart law. In this article, we will study the Biot-Savart law, the direction of the magnetic field induced due to a current carrying element, features of the Biot-Savart law, similarities and dissimilarities between the Biot-Savart law and Coulomb's law, and special cases of the Biot-Savart law.

## Biot-Savart Law Definition

Before understanding Biot-Savart law, let's briefly explain what we mean by a magnetic field

The magnetic field is a physical quantity describing the strength of the magnetic force at each point over space.

Hans Christian Oersted discovered the magnetic effect of a current-carrying wire. Oersted's experiment confirms the formation of a magnetic field around a current-carrying wire with the deflection of a magnetic needle placed near the wire.

The Biot-Savart law helps to calculate the magnetic field around this current-carrying wire.

According to Biot-Savart law, the magnetic field induced due to a current element depends upon the length of the current carrying element, the current's magnitude, direction, and proximity.

## Biot Savart Law Derivation

Let's consider a small current element $$\mathrm{AB}$$ of a conducting wire $$\mathrm{XY}$$ carrying current $$I$$. The length of an infinitesimally small element is $$\mathrm{d}\vec{l}$$. Let $$\vec{r}$$ be the position vector of an observation point P from the current element. Let $$\theta$$ be an angle between $$\mathrm{d}\vec{l}$$ and $$\vec{r}$$. Fig. 2 - The figure shows a small current element on a conducting wire carrying current $$I$$ and an observation point P for an induced magnetic field.

Biot-Savart law states that the magnetic field induced at point P due to a current-carrying wire is

1. directly proportional to the current $$I$$,

2. directly proportional to the length of a current element $$\mathrm{d}\vec{l}$$,

3. directly proportional of sine of angle between $$\vec{r}$$ and $$\mathrm{d}\vec{l}$$,

4. inversely proportional to the square of the position vector, i.e., $$r^2$$.

The mathematical form of Biot-Savart law is

$\mathrm{d}\vec{B}\propto\frac{I\mathrm{d}\vec{l}\sin{\left(\theta\right)}}{r^2}$

or

$\mathrm{d}B=K\frac{I\mathrm{d}l\sin{\left(\theta\right)}}{r^2}$

Where $$K$$ is a proportionality whose value depends upon the medium between the point P and the current element $$\mathrm{d}\vec{l}$$. It is defined as $K=\frac{\mu_0}{4\pi},$

where $$\mu_0=4\pi\times10^{-7}\,\mathrm{T\,A^{-1}\,m^{-1}}$$ is the magnetic permeability of free space/vacuum.

(Video) Applications of Biot-Savart Law

## Biot-Savart Law Formula

Let's take a look at how the Biot-Savart Law can give us a formula for the total magnetic field around a current carrying wire.

### Superposition Principle

Biot-Savart law follows the superposition principle. According to this law, the net magnetic field at the point due to several current elements is the algebraic sum of a magnetic field due to each current element.

Let $$\mathrm{d}\vec{B_1},\mathrm{d}\vec{B_2},\mathrm{d}\vec{B_3},...$$ and so on are the magnetic field at the point P due to the current elements $$I\mathrm{d}\vec{l_1},I\mathrm{d}\vec{l_2},I\mathrm{d}\vec{l_3},...$$ and so on. Then the net magnetic field at point P is

$\mathrm{d}\vec{B}=\mathrm{d}\vec{B_1}+\mathrm{d}\vec{B_2}+\mathrm{d}\vec{B_3}+...$

This equation shows the superposition principle/vector addition.

When considering the magnetic field over a length of wire as we do in the Biot-Savart law, we split up the wire into elements of infinitesimal length $$\mathrm{d}\vec{l}$$. Each of these infinitesimal lengths adds a contribution to the magnetic field of:$\mathrm{d}\vec{B}=\frac{\mu_0}{4\pi}\frac{I\mathrm{d}\vec{l}\sin{\left(\theta\right)}}{r^2}$

To find the overall magnetic field field from a wire we us the superposition principle by integrating over the wire length:

$\vec{B}(\vec{r})=\int\frac{\mu_0}{4\pi}\frac{I\mathrm{d}\vec{l}\sin{\left(\theta\right)}}{r^2}$

## Direction of Magnetic Field

In the Biot-Savart law, the magnetic field due to a current-carrying conductor is given by

$\mathrm{d}\vec{B}=\frac{\mu_0}{4\pi}\frac{I\mathrm{d}\vec{l}\times\vec{r}}{r^3}$

This equation shows that the direction of a magnetic field is along the direction of a cross product $$I\mathrm{d}\vec{l}\times\vec{r}$$. To find the direction of this cross-product, we can use the Right-Hand rule.

According to the Right-Hand Rule, if you point your thumb in the direction of the current then curling your fingers will give the direction of the magnetic field as it curls around the wire.

For the case shown in figure 2, by using the Right-Hand Rule, the curl of your fingers is along a clockwise direction on the plane containing $$\mathrm{d}\vec{l}$$ and $$\vec{r}$$. Then the direction of $$\mathrm{d}\vec{B}$$ is perpendicular to the plane and is directed inward.

### In case when $$\theta=0^\circ$$

The direction of current element $$\left(I\mathrm{d}\vec{l}\right)$$ is along the direction of position vector $$\vec{r}$$, then

\begin{align*}\mathrm{d}\vec{B}&=\frac{\mu_0}{4\pi}\frac{I\mathrm{d}\vec{l}\sin{\left(0^\circ\right)}}{r^2}\\\mathrm{d}\vec{B}&=0\end{align*}

This gives the minimum value of a magnetic field.

### In case when $$\theta=90^\circ$$

The direction of the current element $$\left(I\mathrm{d}\vec{l}\right)$$ is perpendicular to the direction position vector $$\left(\vec{r}\right)$$, then

\begin{align*}\mathrm{d}\vec{B}&=\frac{\mu_0}{4\pi}\frac{I\mathrm{d}\vec{l}\sin{\left(90^\circ\right)}}{r^2}\\\mathrm{d}\vec{B}&=\frac{\mu_0}{4\pi}\frac{I\mathrm{d}\vec{l}}{r^2}\end{align*}

(Video) Biot Savart law (vector form) | Moving charges & magnetism | Khan Academy

This gives the maximum value of a magnetic field.

## Biot-Savart Law and Coulomb's Law

According to Biot-Savart law, the magnetic field around a current-carrying element $$\left(I\mathrm{d}\vec{l}\right)$$ at a distance of $$r$$ is

$\mathrm{d}\vec{B}=\frac{\mu_0}{4\pi}\frac{I\mathrm{d}\vec{l}}{r^2}$

or

$\mathrm{d}\vec{B}=\frac{\mu_0}{4\pi}\frac{I\mathrm{d}\vec{l}\times\vec{r}}{r^3}$

According to Coulomb's law, the electric field around an electric charge $$q$$ at a distance of $$r$$ is

$E=\frac{1}{4\pi\epsilon_0}\frac{q}{r^2}$

or

$\vec{E}=\frac{1}{4\pi\epsilon_0}\frac{q}{r^3}\vec{r}$

Some of the main similarities between Biot-Savart law and Coulomb's law are,

1. In both laws, fields are inversely proportional to the square of the distance from the source (which generates the field) to the test point (where the field is measured).

2. Both laws obey the superposition principle.

3. In the Biot-Savart law, the magnetic field varies directly with its source, which is current element $$\left(Idl\right)$$, and in Coulomb's law, the electric field varies directly with its source, which is electric charge $$\left(q\right)$$.

Some of the main differences between Biot-Savart law and Coulomb's law are,

 S. no. Biot-Savart Law Coulomb's Law 1. The magnetic field is produced by vector source, i.e., current element $$\left(I\mathrm{d}\vec{l}\right)$$. A scalar source produces the electric field, i.e., electric charge $$q$$. 2. The direction of a magnetic field is perpendicular to the plane containing $$I\mathrm{d}\vec{l}$$ and $$\vec{r}$$. The direction of an electric field is along the line joining a source and a test point. 3. The magnetic field produced due to a current element is angle dependent. The electric field produced due to an electric charge does not depend upon an angle. 4. The magnetic field depends on the current flowing and so depends on both the magnitude and velocity of charge. Coulomb's law only depends on the magnitude of charge and considers static charges rather than moving current.

## Applications of Biot-Savart Law

There are several applications of Biot-Savart law but the most important is it helps in calculating the magnetic due to a current element irrespective of its configuration. In other words, Biot-Savart law is independent of the configuration of the wire-carrying current. In this article, we will calculate the induced magnetic field due to a straight wire carrying current and a current carrying in form of a circular coil using Biot-Savart law.

### For a Straight Wire Carrying Current

Imagine a straight current-carrying wire XY in a plane carrying current $$I$$. Let P be a point perpendicular to the wire on a plane at a distance of $$r$$ from the wire and $$I\mathrm{d}\vec{l}$$ be a small current element.

Let $$\vec{r}'$$ be the position vector of point P from the current element. Fig. 4 - The figure shows a straight wire carrying current and an observation point P at a distance of $$r$$ from the wire.

In the diagram, we can see $$\theta$$ is an angle between position vector $$\vec{r}'$$ and a current element $$I\mathrm{d}\vec{l}$$ and $$\phi$$ is an angle between position vector $$\vec{r}'$$ and $$\vec{r}$$.

According to Biot-Savart law, the magnetic field $$\mathrm{d}B$$ at a point P due to the current element $$I\mathrm{d}\vec{l}$$ is$\mathrm{d}\vec{B}=\frac{\mu_0}{4\pi}\frac{I\mathrm{d}\vec{l}\times\vec{r}'}{r'^3}$

(Video) Law of Biot-Savart

or$\mathrm{d}\vec{B}=\frac{\mu_0}{4\pi}\frac{I\mathrm{d}\vec{l}\sin{\theta}}{r'^2}\tag{1}$

From a right-angle triangle CPO,

\begin{align*}\theta+\phi+90^{\circ} &=180^\circ\\\theta &=90^{\circ}-\phi\end{align*}

Substituting this value of $$\theta$$ in equation (1), \begin{align*}\mathrm{d}\vec{B} &=\frac{\mu_0}{4\pi}\frac{I\mathrm{d}\vec{l}\sin{90^{\circ}-\phi}}{r'^2}\\\mathrm{d}\vec{B} &=\frac{\mu_0}{4\pi}\frac{I\mathrm{d}\vec{l}\cos{\phi}}{r'^2}\tag{2}\end{align*}

Also in triangle CPO \begin{align*}\cos{\phi}&=\frac{r}{r'}\\r'&=\frac{r}{\cos{\phi}}\tag{3}\end{align*}

And \begin{align*}\tan{\phi}&=\frac{l}{r}\\l&=r\tan{\phi}\tag{4}\end{align*}

By differentiating equation (4) $\mathrm{d}l=r\sec^2{\phi}d\phi\tag{5}$

using equations (3) and (5), equation (2) becomes\begin{align*}\mathrm{d}B &= \frac{\mu_0}{4\pi}\frac{Ir\sec^2{\phi}\cos{\phi}}{\frac{r^2}{\cos^2{\phi}}}\mathrm{d}\phi\\\mathrm{d}B &= \frac{\mu_0}{4\pi}\frac{Ir\cos{\phi}\mathrm{d}\phi} {\cos^2{\phi}}\frac{\cos^2{\phi}}{r^2}\\\mathrm{d}B &= \frac{\mu_0}{4\pi}\frac{I}{r}\cos{\phi}\mathrm{d}\phi\tag{6}\end{align*}

By integrating equation (6) with the limit $$-\phi_1$$ and $$+\phi_2$$, the magnetic field at the point P due to a whole straight is

\begin{align*}\int_{-\phi_1}^{\phi_2} \mathrm{d}B &= \frac{\mu_0}{4\pi}\frac{I}{r} \int_{-\phi_1}^{\phi_2} \cos{\left(\phi\right)} \mathrm{d}\phi\\B&=\frac{\mu_0}{4\pi}\frac{I}{r}\left[\sin{\phi}\right]_{-\phi_1}^{\phi_2}\\B&=\frac{\mu_0}{4\pi}\frac{I}{r}\left(\sin{\left(\phi_2\right)}-\sin{\left(-\phi_1\right)}\right)\\B&=\frac{\mu_0}{4\pi}\frac{I}{r}\left(\sin{\left(\phi_2\right)}+\sin{\left(\phi_1\right)}\right)\end{align*}This equation gives the magnetic field at point P due to a finite straight wire XY carrying current.

Let's say conductor XY is of infinite length. In this case $$\phi_1=\phi_2=90^\circ$$, the magnetic field at the point P will become

\begin{align*}B&=\frac{\mu_0}{4\pi}\frac{I}{r}\left(\sin{\left(90^\circ\right)}+\sin{\left(90^\circ\right)}\right)\\B&=\frac{\mu_0}{4\pi}\frac{I}{r}2\\B&=\frac{\mu_0}{2\pi}\frac{I}{r}\end{align*}

The direction of this magnetic field is perpendicular to the plane containing the wire and an observation point.

### Current Carrying Circular Coil

Let's say a circular coil of radius $$r$$ is placed perpendicular to the plane of the paper. $$I$$ be the current flowing through the coil. Suppose an observation point P is on the paper at the distance of $$x$$ from the center of the coil (let's say O). Fig. 5 - The figure shows the magnetic field at point P due to a current-carrying circular coil.

In the diagram, we can see that the current on the wire is perpendicular to the position vector $$\vec{MP}$$. Thus, the angle between $$I\mathrm{d}\vec{l}$$ and $$\vec{MP}$$ is $$90^\circ$$.

By using Biot-Savart law, the magnetic field at the point P due to a small current element at the point M in the diagram is

\begin{align*}\mathrm{d}\vec{B}&=\frac{\mu_0}{4\pi}\frac{I\mathrm{d}\vec{l}\sin{\left(90^\circ\right)}}{\left(\sqrt{r^2+x^2}\right)^2}\\\mathrm{d}\vec{B}&=\frac{\mu_0}{4\pi}\frac{I\mathrm{d}\vec{l}}{\left(r^2+x^2\right)}\tag{7}\end{align*}

Using Right Hand Rule, the direction of this magnetic field is perpendicular to the plane containing the current element $$I\mathrm{d}\vec{l}$$ at M and a position vector $$\vec{MP}$$.

(Video) Biot Savart Law and its Applications

By resolving this magnetic field along the X and Y axis as shown in the figure, we got $$\mathrm{d}B\cos{\left(\phi\right)}$$ along the Y-axis and $$\mathrm{d}B\sin{\left(\phi\right)}$$ along the X-axis.

Similarly, due to a current element at N, the component of a magnetic field is $$-\mathrm{d}B\cos{\left(\phi\right)}$$ along the Y-axis and $$\mathrm{d}B\sin{\left(\phi\right)}$$ along the X-axis.

Therefore, the net magnetic field along the Y-axis is

$\mathrm{d}B_{\mathrm{y}}=\mathrm{d}B\cos{\left(\phi\right)}-\mathrm{d}B\cos{\left(\phi\right)}=0$

And the magnetic field along the X-axis is

$\mathrm{d}B_{\mathrm{x}}=\mathrm{d}B\sin{\left(\phi\right)}+\mathrm{d}B\sin{\left(\phi\right)}=2\mathrm{d}B\sin{\left(\phi\right)}$

So, the net magnetic field at point P due to the current element at M and its alternate on the coil (i.e. at N) is

\begin{align*}\mathrm{d}B_{\mathrm{net}}&=\mathrm{d}B_{\mathrm{y}}+\mathrm{d}B_{\mathrm{x}}\\\mathrm{d}B_{\mathrm{net}}&=0+2\mathrm{d}B\sin{\left(\phi\right)}\\\mathrm{d}B_{\mathrm{net}}&=2\mathrm{d}B\sin{\left(\phi\right)}\tag{8}\end{align*}

Using equation (7), equation (8) becomes

$\mathrm{d}B_{\mathrm{net}}=2\times \frac{\mu_0}{4\pi}\frac{I\mathrm{d}\vec{l}\sin{\left(\phi\right)}}{\left(r^2+x^2\right)}$

From triangle MPO, $$\sin{\left(\phi\right)}=\frac{r}{\sqrt{r^2+x^2}}$$, thus, $$\mathrm{d}B_{\mathrm{net}}$$ becomes

$\mathrm{d}B_{\mathrm{net}}=2\frac{\mu_0}{4\pi}\frac{Ir\mathrm{d}\vec{l}}{\left(r^2+x^2\right)^{3/2}}$

For the half current-carrying coil and its alternate part (another half of the coil), the net magnetic field at point P is

\begin{align*}\int \mathrm{d}B_{\mathrm{net}}&=2\frac{\mu_0}{4\pi}\frac{Ir}{\left(r^2+x^2\right)^{3/2}}\int \mathrm{d}\vec{l}\\B_{\mathrm{net}}&=2\frac{\mu_0}{4\pi}\frac{Ir}{\left(r^2+x^2\right)^{3/2}}\pi r\\B_{\mathrm{net}}&=\frac{\mu_0}{2}\frac{Ir^2}{\left(r^2+x^2\right)^{3/2}}\end{align*}

If point P is at the center of a coil, i.e., $$x=0$$, the net magnetic field at point P due to a current-carrying circular coil is

\begin{align*}B_{\mathrm{net}}&=\frac{\mu_0}{2}\frac{Ir^2}{\left(r^2+0\right)^{3/2}}\\B_{\mathrm{net}}&=\frac{\mu_0}{2}\frac{Ir^2}{r^3}\\B_{\mathrm{net}}&=\frac{\mu_0}{2}\frac{I}{r}\end{align*}

For $$n$$ number of turns in the coil

$B_{\mathrm{net}}=\frac{\mu_0}{2}\frac{nI}{r}$

This equation shows the magnetic field at the center of the current-carrying coil having $$n$$ number of turns which is calculated using Biot-Savart law.In conclusion, Biot-Savart law helps in calculating the magnetic field due to a current-carrying conductor irrespective of its configuration.

## Biot Savart Law - Key Takeaways

• The magnetic field is the space around a magnet or a current-carrying wire in which its magnetic effects can be felt.
• According to Biot-Savart law, the magnetic field induced due to a current element depends upon the current's length, magnitude, direction, and proximity as $$\mathrm{d}B=K\frac{Idl\sin{\left(\theta\right)}}{r^2}$$.
• Biot-Savart law follows the superposition principle.
• The direction of a magnetic field obtained from Biot-Savart Law is represented by the Right-Hand Rule/Right-handed screw rule.
• According to Right-Hand Rule, stretch the thumb of your right hand and curl the rest of your fingers in the direction from $$\mathrm{d}\vec{l}$$ towards $$\vec{r}$$. Then the thumb will point in the direction of a magnetic field.
• Biot-Savart law is applicable only in symmetrical current distribution on conductors.
• Biot-Savart law applies only to very small lengths of current elements on conductors and is analogous to Coulomb's law in electrostatics.
• Biot-Savart law is independent of the configuration of the wire-carrying current.
(Video) Electro Magnetics Theory - Biot Savart's Law

## References

1. Fig. 1 - Closed Up Photography of Brown Wooden Framed Sony Speaker (https://www.pexels.com/photo/closed-up-photography-of-brown-wooden-framed-sony-speaker-157534/) by Anthony : ) (https://www.pexels.com/@inspiredimages/) under the Pexels license (https://www.pexels.com/license/).
2. Fig. 2 - Magnetic field due to small current element, StudySmarter Originals.
3. Fig. 3 - Right-Hand Rule/Right-handed screw rule, StudySmarter Originals.
4. Fig. 4 - Magnetic field due to a straight wire carrying current, StudySmarter Originals.
5. Fig. 5 - Magnetic field due to a current carrying circular coil, StudySmarter Originals.

## FAQs

### Biot Savart Law: Meaning & Applications? ›

What is Biot-Savart Law? Biot-Savart's law is an equation that gives the magnetic field produced due to a current carrying segment. This segment is taken as a vector quantity known as the current element.

What is Biot-Savart law and its applications? ›

Biot Savart's Law helps to calculate the resultant magnetic field B at position r in the three-dimensional space. The magnetic field is generated due to a flexible wire, which carries current. The steady current in the wire is the continual flow of charge, which does not change with time.

What is the use of Biot-Savart law in real life? ›

Biot Savart Law is used in the calculation of the magnetic field generated by an electric current. The law can be used to determine the strength and direction of the magnetic field at any point in space. Additionally, Biot Savart Law can be used to calculate the force on a moving charge in a magnetic field.

What is the definition and explanation of Biot-Savart law? ›

Biot savart law states that “ magnetic field due to a current-carrying conductor at a distance point is inversely proportional to the square of the distance between the conductor and point, and the magnetic field is directly proportional to the length of the conductor, current flowing in the conductor”.

Biot-Savart law's advantage is that it works with any magnetic field produced by a current loop. The disadvantage is that it can take a long time. Describe the magnetic field due to the current in two wires connected to the two terminals of a source of emf and twisted tightly around each other.

What is the difference between Ampere's law and Biot-Savart law? ›

The Biot-Savart law considers the contribution of each element of current in a conductor to determine the magnetic field, while for Ampere's law, one need only know the current passing through a given surface.

What is a real life example of Ampere's law? ›

It has to do with an electric current creating a magnetic field. If you ever wrapped an insulated wire around a nail and connected a battery to it you have experienced Ampère's Law. In fact, electric current is today measured in amperes or amps for short. Ampère developed this equation by experimenting with magnets.

What is the application of Biot-Savart law to current carrying loop? ›

Application of Biot- Savart Law

This law is used to determine the magnetic fields in space due to any current carrying conductor. This Law is used to determine the force between two long and parallel current carry conductors. This law is also used to calculate the Magnetic field on the axis of a circular current loop.

What is Biot-Savart law equivalent to? ›

Solution : Ampere's circuital law is equivalent to Biot-Savart law.

What is the other name of Biot-Savart law? ›

Biot Savart law is also known as Laplace's law or Ampere's law. Consider a wire carrying an electric current I and also consider an infinitely small length of a wire dl at a distance x from point A.

### What is the Biot-Savart law basic formula? ›

The Biot-Savart law starts with the following equation: →B=μ04π∫wireId→l×ˆrr2. B=μ04π∫wireIrdθr2. The current and radius can be pulled out of the integral because they are the same regardless of where we are on the path.

What are three similarities between Biot-Savart law and Coulomb's law? ›

(1) Both depend inversely on the square of distance. (2) Both are long range. (3) The principle of superposition applies to both fields.

What is the validity of Biot-Savart law? ›

The law is valid in the magnetostatic approximation, and consistent with both Ampère's circuital law and Gauss's law for magnetism. It is named after Jean-Baptiste Biot and Félix Savart, who discovered this relationship in 1820.

Which property Cannot be calculated from Biot-Savart law? ›

Solution: The Biot-Savart law cannot be used to determine the intensity of an electric field.

How do you know when to use Biot-Savart law? ›

We can use Biot–Savart law to calculate magnetic responses even at the atomic or molecular level. It is also used in aerodynamic theory to calculate the velocity induced by vortex lines.

Is Biot-Savart law and Laplace law same? ›

In 1820 Oersted found that when current in passes through a conductor, magnetic field is produced around it. Just at the same time, Laplace gave a rule for calculation magnitude of magnetic field produced. It is known as Laplace's law or Biot-Savart's law.

Can Ampere's law be derived from Biot-Savart law? ›

It is expressed in terms of the line integral of →B and is known as Ampère's law. This law can also be derived directly from the Biot-Savart law. We now consider that derivation for the special case of an infinite, straight wire. →B⋅d→l=Brdθ.

What is Ampere's law in simple words? ›

Ampere's Law can be stated as:

The magnetic field created by an electric current is proportional to the size of that electric current with a constant of proportionality equal to the permeability of free space.”

What was the problem with Ampere's law? ›

The inconsistency of this law is that it is logically incorrect. This law is true only for steady currents. Understanding this inconsistency, Maxwell included time-varying electric fields into the law. While charging a conductor using the current-carrying coil, there is current between the plates of the capacitor.

Why do we need Ampere's law? ›

Ampere's Law allows us to bridge the gap between electricity and magnetism; that is, it provides us with a mathematical relation between magnetic fields and electric currents. It gives us a way to calculate the magnetic field that is produced as a result of an electric current moving through a wire of any shape.

### What are the advantages of Ampere's law over Biot-Savart law? ›

Ampere's circuital law proves to be most useful to find magnetic fields in those cases in which the magnetic fields are highly symmetrical. The Biot-Savart law allows us to calculate the magnetic field resulting from a current-carrying wire of any shape, but the calculation may become complicated.

How is Biot-Savart law used in determining the magnetic field in a certain region? ›

A current in a loop produces magnetic field lines B that form loops around the current. The Biot-Savart law expresses the partial contribution dB from a small segment of conductor to the total B field of a current in the conductor.

How was Biot-Savart law invented? ›

In 1820 he and the physicist Félix Savart discovered that the intensity of the magnetic field set up by a current flowing through a wire is inversely proportional to the distance from the wire. This relationship is now known as the Biot-Savart law and is a fundamental part of modern electromagnetic theory.

What is the application of Biot-Savart law for solenoid? ›

A solenoid is formed by wrapping wire around a tube with the windings closely spaced. Applying the Biot-Savart law to this helical wire reveals that for a long, tightly wound solenoid, the field is very strong and very uniform inside the tube, and very weak outside the tube.

What is the Biot-Savart law application of straight wire? ›

Biot Savart's law states the relationship between a current-carrying wire and a point P placed at a distance r from the wire. The magnitude of this magnetic field is inversely proportional to the square of the distance of wire to the point P kept at distance r.

What are 2 applications of solenoid? ›

• A solenoid is a basic term for a coil of wire that we use as an electromagnet.
• Solenoids are used in MRI machines which help in creating MRI images.
• It is also used in electric bells, electric switches, motors, etc.

What is the real life application of solenoid? ›

Solenoids are frequently used in locking mechanisms, and the scope of locking applications includes many industries. Obvious uses include door locking, in hotels, offices and secure areas, vending machines, remote access systems, turnstiles, car park and access barriers.

How is the Biot Savart law used in determining the magnetic field? ›

Biot Savart law states that the magnetic field due to a tiny current element at any point is proportional to the length of the current element, the current, the sine of the angle between the current direction and the line joining the current element and the point, and inversely proportional to the square of the ...

Does a straight wire create magnetic field? ›

Magnetic field of a wire. Magnetic fields arise from charges, similarly to electric fields, but are different in that the charges must be moving. A long straight wire carrying a current is the simplest example of a moving charge that generates a magnetic field.

What is one application of Ampere's law? ›

Applications of Ampere's Law

Ampere's Law is used to : Determine the magnetic induction due to a long current-carrying wire. Determine the magnetic field inside a toroid. Determine the magnetic field created by a long current-carrying conducting cylinder.

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