6 Biot Savart’s Law:-^m.imp

As we know when current passes through a conductor, then magnetic field set up around the conductor which was firstly calculated by Jean Biot & Felix Savart called Biot Savart’s Law.

$F:\unit 3\New folder\New folder\37.jpg$ According to this law, the magnitude of magnetic field d at a point due to current following through a conductor is depends upon, current , length of conductor, distance of point from conductor & angle between point and conductor as

Combining all eqⁿs we get

Or =

Where K = = 10^-7TmA^-1

Here u₀ called permeability of free space.

So Biot Savart’s law become

In vector form

The direction of dB can be given by right hand rule.

^Imp.In present case the direction of is perpendicular to plane of paper containing both & in inward direction; if P point lies in L.H.S then in outwards direction.

Special cases:-

I,e. magnetic field at a point perpendicular to current element is maximum

 This law is applicable for infinite small conductor.

 This law is similar to coulomb’s law in electrostatics.

 This law is difficult to verify experimentally because it is difficult to construct infinite small conductor.

7 Biot Savart’s law V/s Coulomb’s Law:-

As according to Coulomb’s Law

& from Biot Savart’s law

dB =

On comparing above eqⁿs we can give similarity & dissimilarity between both.

Similarity

Both the law obey inverse square law (α )
Both the law obeys principle of Superposition.

Dissimilarity:-

The source of magnetic field is current while source of electric field is charged.
Electric field exists due to both rest & motion of charge while magnetic field exists due to motion of charge.
The magnetic field is angle dependent while electric field is not.

8 Magnetic field due to a long straight Conductor carrying current:-^m.imp

Suppose a point P having a distance a from the straight conductor carrying current I, then according to Biot savart Law, the magnetic field at P due to small current element , r distance apart is

$F:\unit 3\New folder\New folder\35.jpg$ –(1)

Now from Δ COP

Or (i)

Also

(ii)

As tan =

⇒ = a tan

Differentiating both side d =a sec² .d (iii)

Using all values in eqⁿs (1) we get

Or =

To calculate complete magnetic field integrating both sides we get

B =

B = [Sin₂– Sin(-∅₁)]

Or B = [Sin∅₁+ Sin∅₂]

The direction of B can be given by Right hand rule.

Special cases:-

If the conductor is infinite long & point P lies near to the dipole then

B = [sin90⁰+ sin90⁰]

Or B = =

If the conductor is infinite long but P lies near end y then ∅₁= 90, ∅₂=0

B = [sin90+ sin0]

Q1. A current of 10A is flowing from east to west in a long straight wire kept on a horizontal table. The magnetic field developed at a distance 10cm vertically above the wire is:

Ans:

Q2. A straight wire of mass 200 g and length 1.5 m carries a current of 2 A. It is suspended in mid-air by a uniform horizontal magnetic field B (Fig. 4.3). What is the magnitude of the magnetic field?

Solution we find that there is an upward force F, of magnitude, for mid-air suspension, this must be balanced by the force due to gravity:

⇒

0.65 T

Note that it would have been sufficient to specify, the mass per unit length of the wire. The earth’s magnetic field is approximately 4 × 10^–5T and we have ignored it.

Q3. An element is placed at the origin and carries a large current I = 10 A. What is the magnetic field on the y-axis at a distance of 0.5 m. ∆x = 1 cm.

Solution here

⇒

The direction of the field is in the +z-direction.

9 Magnetic field At the Center Of The Circular Coil Carrying current:-^m.imp

$F:\unit 3\New folder\New folder\33.jpg$ According to Biot Savart Law, the magnetic field at the center of circular coil carrying current can be given as

–(1)

(Here is angle between current element Id & r. )

As radius is always perpendicular to tangent

so θ= 90⁰ ⇒ sin90= 1

To calculate complete magnetic field, integrate both sides

⇒ B =ʃ

Here ʃ circumference of circle

⇒ B =r

Or B =

If the circular coil contains n turns then

B =

or B=

Here the direction of magnetic field can be given by right hand rule.

Q4. The magnetic dipole moment of a current carrying coil does not depend upon:

A Number of turns of the coil

B Cross-sectional area of the coil

C Current flowing in the coil

D Material of the turns of the coil

Q5. An electron is revolving around the nucleus in a circular orbit with a speed of m/s . If the radius of the orbit is m, find the current constituted by the revolving electron in the orbit

Solution

Q6. A steady current of 2A flows through a circular coil having 5 turns of radius 7cm. The coil lies in X-Y plane with its centre at the origin. Find the magnitude and direction of the magnetic dipole moment of the coil.

Ans:

Q7. Consider a tightly wound 100 turns coil of radius 10 cm, carrying a current of 1 A. What is the magnitude of the magnetic field at the centre of the coil?

Solution Since radius r = 10 cm = 0.1 m. The number of turns n = 100.

So B=

10 Magnetic field at a point on the axis of a circular coil carrying current:-

Suppose a point P on the axis of a Circular coil carrying current I. Suppose two small current element & on coil. Then the Magnetic field due to these current Elements at P is dB & dB’. As shown in fig.

Clearly dB & dB’ are equal. Resolving dB & dB’ into rectangular components, we see that & are equal & opposite so they are cancelled out.

So the total magnetic induction at P due to current through the whole circular coil is given

B =ʃdB Sin∅ –(i)

From Ampere circuital law, the magnetic induction due to at P is

$F:\unit 3\New folder\New folder\34.jpg$

Here is angle between r & so 90⁰.

So dB =

Using in (i)

B = ʃ

Here sin∅ & ʃ d =2

⇒ B =. 2

If there are n turn in the coil

then B =

 at center =0 ⇒

B =

 If P point lies far away from the coil then a so a can be neglected

⇒ B =

 If P point lies at a distance equal to radius of the coil I,e. r = a we have

⇒ B=

11 The direction of magnet field due to circular coil:-^m.imp

As we can see the magnetic lines form Close loop at the end of the circular coil & straight line at the center of the loop. The direction of these magnetic lines can be given by Right hand rule.

$F:\unit 3\New folder\New folder\28.jpg$

12 Right hand rule:-

Suppose the current is flowing through a circular conductor, if we imagine the fingers of the right hand curling in the direction of current, then the thumb will point in the direction of magnetic field.

13 Clock rule:-

According to clock rule if current moves in anti clock wise direction, the upper face of loop or coil is behave as north pole & when current moves in clock wise direction, then upper face behave as south pole.

$F:\unit 3\New folder\New folder\29.jpg$

Biot Savart’s Law

6 Biot Savart’s Law:-^m.imp

Chapter 4 Moving Charges and Magnetism

class 12 physics notes

6 Biot Savart’s Law:- m.imp

Chapter 4 Moving Charges and Magnetism

class 12 physics notes

6 Biot Savart’s Law:-^m.imp