Biot Savart’s law and its Applications

Physics Chemistry Biology Mathematics
Science > Physics > Magnetic Effect of Electric CurrentYou are Here

Oersted’s Experiment:

  • Oersted took long conducting wire and aligned it in magnetic meridian i.e. along the north-south direction. He put magnetic needle exactly below the conductor. The magnetic needle aligned itself in the north-south direction such that both the conductors and the magnetic needle are parallel to each other.

Magnetic Effect 01

  • When a current is passed through the conductor there was a deflection in the magnetic needle. When the current was switched off the magnetic needle came back to its original position.
  • When the direction of current was reversed the direction of deflection of the magnetic needle was also reversed.
  • When the magnetic needle is put exactly above the conductor keeping the direction of current same, the direction of deflection of the magnetic needle was reversed.
  • When the distance of the magnetic needle is increased the deflection of the magnetic needle decreased.

Conclusions:

  • Initially the magnetic needle aligns itself in magnetic meridian due to action of earth’s magnetic field on the needle.
  • After passing current through the conductor there is a deflection in the magnetic needle and when the current is switched off there is no deflection in the magnetic needle which indicates that due to the flow of current in conductor there is a creation of magnetic field around the conductor.
  • If the direction of current is reversed deflection of the needle is also reversed which indicates that if the direction of current in the conductor is reversed there is reversal of direction of magnetic field around the conductor.
  • The direction of deflection of needle depends upon the position of the needle i.e. whether it is kept above or below the conductor.
  • If the conductor is aligned in the east – west direction and current is passed through it, then there is no deflection.

To Find the Direction of Deflection of Magnetic Needle:

Swim rule:

  • Imagine a person swimming along the wire in the direction of current with his face towards the needle, then the north pole of the needle will be deflected towards his left hand.

Right-hand palm rule:

  • Hold your right-hand palm along a conductor such that fingers are indicating the direction of current and palm facing conductor then the north pole deflect in the direction of outstretched thumb.

Direction of Magnetic Field (Magnetic Induction):

Right-Hand Thumb Rule Or Right-Hand Grip Rule:

  • Hold the current carrying conductor in your right hand such that the outstretched thumb indicates the direction of the current, then the direction of curled fingers indicate the direction of the magnetic field created by the conductor.

Magnetic Effect 02

Right-hand Screw Rule:

  • Imagine that right-hand screw is held with its axis parallel to the direction of the conductor is rotated with fingers such that the tip of the screw move in the direction of the current. Then the direction in which the fingers rotate the head gives the direction of magnetic induction.

Magnetic Effect 03

Factors Influencing the Strength of Magnetic Field:

  • The magnetic field created due to current carrying straight conductor is in the form concentric circles whose direction is given by Right-hand thumb rule.
  • The strength of magnetic field depends on the current through the conductor. If the current increases, the strength of magnetic fields increases. When the current through the conductor decreases there is a decrease in the strength of magnetic field.
  • The strength of magnetic field at a point depends on the distance of the point from the current carrying conductor. If the distance increases the strength of magnetic field decreases and as the distance decreases the strength of magnetic field increases.


Magnetic Induction:



  • The magnetic induction at any point in the magnetic field is defined as the magnetic flux passing through the unit area at that point.
  • It is denoted by letter “B”. It is a vector quantity. Its S.I. unit is Wb/m² or tesla (T).
  • Mathematically,

B = ∅ /A

Where  B = Magnetic induction,  ∅= Magnetic flux

A = Area through which magnetic flux is passing

Biot Savart’s law (Laplace’s Law):

  • The magnetic induction at a point  near current carrying conductor is directly proportional to
    • The current in the element (I)
    • The length of the element (dl)
    • The sine of the angle between the element and the straight line joining the element to the point.
    • and inversely proportional to the square of the distance between the element and the point..

Magnetic Effect 04



Explanation:

  • Consider conductor of any shape in form of wire. Let i be the current through the conducting wire. Let dl be a small element of the conductor, then the quantity i.is known as the current element of the conductor. Let P be the point at which magnetic induction due to current carrying conductor is to be found. Let be the position vector of point  P with respect to the current element i.dl. Let θ be the angle between dl and r, then by Biot Savart’s law the magnetic induction due to the small element dl is given by

dB ∝ i           …………….. (1)

dB ∝ dl               ……………(2)

dB ∝ sinθ        ……………(3)

dB ∝ 1/r²            ……………(4)

From equations (1), (2), (3) and (4)



Magnetic Effect 05

This is a mathematical expression for the Biot-Savart’s law.

Magnetic Effect 06

This is a mathematical expression for the Biot-Savart’s law in vector form.

The total magnetic induction due to current in the whole conductor is given by



Magnetic Effect 07

Magnetic Induction at a Point Near an Infinitely Long Straight Current Carrying Conductor:

  • Let us consider infinitely long straight conductor carrying current i. Let P be the point at which magnetic induction due to the current carrying conductor is to be found. Let us consider a small element dl of the conductor at O. Let vector AP or vector r be the position vector of point  P with respect to the current element. Let θ be the angle between the position vector of the point P and the current element. Let us draw PC perpendicular to the length of the conductor is drawn such that PC = R  and OC = l.  Now, angle COP = π – θ

Magnetic Effect 08

  • Let dB be the magnetic induction at point ‘P’ due to current carrying conductor it is given by Biot Savart’s law.

Magnetic Effect 09

Magnetic Effect 10

 



 

 

Magnetic Effect 11

Magnetic Effect 13



This is an expression for magnetic induction at the point near infinitely long straight conductor.



Magnetic Induction at Centre of Current Carrying Circular Coil:

  • Consider a current carrying coil having radius R and having a single turn. Let i be the current through this circular coil.  Let  O be the centre of the circular coil at which magnetic induction is to be found.  Let  dl be the small element of current carrying coil at P, let θ be the angle between the current element and line joining the current element with point O.  In this case,  θ = 900.

 

Current Carrying Coil

  • Magnetic induction at point O due to current element i. dl is given by Biot-Savart’s law

Magnetic Effect 16

The total magnetic induction at “O” can be found by integrating both sides.

Magnetic fieldThis is an expression for magnetic induction at centre of current carrying circular coil



Science > Physics > Magnetic Effect of Electric CurrentYou are Here
Physics Chemistry Biology Mathematics

One Comment

  1. Shifa khan

    Its very helpful

Leave a Comment

Your email address will not be published. Required fields are marked *