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Biot Savart Law – Magnetostatics – Magnetic Flux

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. 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. Now let us understand in further details:

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Consider a current carrying conductor in a closed surface.

Mathematically,biot-savart-law explanation

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. magnetostatics

direction of magnetic field

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,

magnetostatics-1-19-638 (1)

 

 

The magnetic flux through a given surface S is given by

magnetostatics-1-19-638

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

∇•B = 0∇ × B = µ0 J —-> ∇• J = 0

 

There are no magnetic flow sources, and themagnetic flux lines always close uponthemselves. There are three ways in which force due to magnetic fields canbe experienced

  1. Due to moving charge particle in a B field
  2. On a current element in an external field
  3. Between two current elements

 

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