## What is Biot-Savart Law?

Biot and Savart conducted many experiments on the force exerted by an electric current on a nearby magnet and at last they derived a mathematical expression that gives the magnetic field at some point in space due to a current passing through a conductor.

**biot savart law statement**

The biot savart law states that:

Magnetic field (B) along vertical current carrying conductor/wire in a closed surface is directly proportional to the current(I) and inversely proportional to the perpendicular distance from the point of conductor/wire.

#### biot savart law derivation

Now let us understand in further details:

Consider a current carrying conductor in a closed surface.

Mathematically,

B∝ I/r

B=KI/r

Where K= propotionality constant and its value depends on nature of closed surface where conducter is situated

K= µ 0 /2 π

µ 0= permiability of free space = 4π x 10e-7 h/m

K= 2 x 10e-7 h/m

B= µ 0 I/2πr

### Magnetostatics

If charges are moving with constant velocity, a static magnetic (or magnetostatic) field is produced. Thus, magnetostatic fields originate from currents (for instance,direct currents in current-carrying wires). Most of the equations we have derived for the electric fields may be readily used to obtain corresponding **equations for magnetic fields** if the equivalent analogous quantities are substituted

The magnetic field intensity dH produced at a point P by the differential current element Idl is proportional to the product of Idl and the sine of the angle α between the element and the line joining P to the element and is inversely proportional to Idl sin α the square of the distance R between P and the element.

#### Difference Between Biot-Savart law and Ampere’s law

Biot-Savart law and Ampere’s law both help in finding magnetic field distributions, but Ampere’s law takes symmetry into account as its a closed line integral (Amperian loop). Both laws can be used to calculate the net magnetic field produced at a point by various distributions of current. Situations where Ampere’s law can be used include Magnetic field of a solenoid and Magnetic field of a toroid.

##### Magnetic Flux Density

The magnetic flux density vector is related to the **magnetic field intensity** H by the following equation

B = µ H, T (tesla) or Wb/m2

Where µ is the permeability of the medium. Except for ferromagnetic materials ( such as cobalt, nickel, and iron), most materials have values of µ very nearly equal to that for vacuum,

The magnetic flux through a given surface S is given by

Law of conservation of magnetic flux or Gauss’s law for magnetostatic field

∇•B = 0∇ × B = µ0 J —-> ∇• J = 0

There are no magnetic flow sources, and the magnetic flux lines always close upon themselves. There are three ways in which force due to **magnetic fields** can be experienced

- Due to moving charge particle in a B field
- On a current element in an external field
- Between two current elements

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