Notes for Magnetism and moving Charge chapter of class 12 physics. Dronstudy provides free comprehensive chapterwise class 12 physics notes with proper images & diagram.

The first evidence of the relationship of magnetism to moving charges was discovered in 1819 by the Danish scientist Hans ChristianÂ Oersted. He found that a compass needle was deflected by a current carrying wire. When the direction of current was reversed the deflection also got reversed.

It turns out that there is no source of magnetic force similar in nature to *point electric charges* giving rise to electric fields. Such *magnetic monopoles* have not been found so far. The elementary source of magnetic force is a current element . The force on another similar conductor can be expressed conveniently in terms of a magnetic field Â due to the first. The properties of this magnetic field are as follows:

1. The magnetic field grows *weaker* as we move *farther*Â from its source. In particular, the magnitude of the magnetic field dB is *inversely proportional* to the *square of the distance from the current element **.
*2. The larger the electric current, the larger is the magnetic field. In particular, the

current I

3. The magnitude of the magnetic field is proportional to sin, where is the angle between the current element Â Â and vector Â that points from the current element to the point in space where *Â is evaluated. The direction of **Â Â is the same as the direction of current at that point.*

4. The direction of the Â is *not radially *away from its source as the gravitational field and the electric field are from their sources. In fact, *the direction *of *Â is **perpendicular* *to both **Â and the vector* .

These features of field Â can be written compactly as

Here, Â is a constant of proportionality and Â is unit vector in the direction of .

The constant Â is called the *permeability of free space* or the *permeability constant*. Its value is

The magnetic field Â is also called ** magnetic induction**, or

Its

The dimensions of Â are [MT

The

According to Biot-Savart law,Â

â¸« Â Â

**Case ( A)** : The point

**Case ( B) :** The point

But ,Â Â Â Â andÂ Â Â Â , .

â¸« Â

or Â

**Note **that

(1) For points along the length of the wire (but not on it) the field is always zero.

(2) For points at a perpendicular distance *d* from the wire, field *B* varies inversely with distance,

Â [and not ].

(3) The field is always perpendicular to the plane containing the wire and the point. So in a plane perpendicular to the wire the lines of force are concentric circles.

(4) If the wire is of ** infinite length** and the point

Â or Â Â

(5)Â IfÂ ** the point is near one end of an infinitely long wire**, and . Hence,

Â or Â Â

(6)Â If the wire is of ** finite length and the point is on its perpendicular bisector,** . Hence,

Â withÂ Â Â Â where *L *is length of the wire.

(7)Â If the wire is of ** finite length and the point is near its one end, ** . Hence,

Â with Â

*Application 1
*

*Solution:*

The right-hand thumb rule shows that the magnetic field at *P* due to each of the wires is perpendicular to the plane of the diagram and is going into it. The magnitude of the field due to each wire is

Â Â Â Â Â Â Â Â Â Â **Â Â Â Â Â Â Â Â Â Â Â Â Â **

Total field due to both the wires is

*Application 2
*

*Solution:*

As point *O* is along the length of segments *L* and *M* so the field at *O* due to these segments will be zero. Further, as the point *O* is near one end of a long wire,**Â **

so Â Â Â Â Â Â Â Â Â [as *RO = SO = d*]

Substituting the given data,

Let *AB* be a circular segment of radius *R*. Point *P* is at its centre. Here,

(*i*) each element is at the same distance from the centre, i.e., *r = R* = constant,

(*ii*) the angle between element Â and Â is always , and

(*iii*) the contribution of each element to Â is in the same direction (i.e., out of the page if the current is anticlockwise and into the page if clockwise).

â¸« Â Â

But ,

â¸« Â Â Â Â Â Â Â Â or Â

**Note** that

(1) The angle is in radians

(2) If the loop is semicircular (i.e, ),Â

(3) If the loop is a full circle with *N* turns (i.e., ),Â

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