## Orested Experiment-

When a conducting wire is connected in an electric circuit where a battery and a key is present in a circuit. A magnetic needle is placed nearby the conducting wire and the key is present. It is observed that there is some deflection in a magnetic needle which implies that there is a magnetic field present around the conducting wire.

When a charged particle moves with the constant velocity it produces an electric field and magnetic field both at the same time. Free electron present in conducting wires moves with a constant velocity which is known as drift velocity while applying a potential difference across the ends of the conducting wire.

The field around a magnetic particle in which another particle experiences magnetic force is called a magnetic field. It is denoted by the ‘b’ vector.

## Biot Savart Law-

For a current element in a current-carrying wire magnetic field at a distance r from the wire is

- Directly proportional to the current I.
- Directly proportional to the element.
- Directly proportional to the sine of angle between dl and r.
- Inversely proportional to the square of the distance between them that is r.

## Differences and Similarities Between Coulomb’s law and Biot Savart Law-

### Similarities –

- Both fields follow inverse Square law.
- Both are large range field.
- principle of superposition is applicable for both electric field and magnetic field.

### Differences –

- The Coulamb’s law is independent of angle where is biot savart law depends on angle.
- Electric field is generated by scalar quantity which is charge when magnetic field is originated by current element and which is vector quantity.

## Magnetic Field Due To A Current-Carrying Wire –

Consider a conducting wire of length infinite in which current ‘I’ is flowing. We need to find the magnetic field at point P which is at a perfect perpendicular distance d from a point o situated on the wire. Let the current element is assumed at a distance l from a point on the wire. Element diesel substance and angle 5 with line API and also describe an angle at point P.

Assume where is of limited where one end of a wire substance angle 51 with line op and other and substance angle fight 2 with the line.

### Magnetic Field Due To A Circular Coil At Its Centre –

Consider a circular coil of radius capital R in which current I is flowing its radius is r. VR to find the magnetic field at its center for which we consider an element DL at its surface. DL is always perpendicular to the r. So, Q is equal to 90 degrees.

## Direction Of Magnetic Field –

There are two routes given for opening the direction of magnetic field –

- Right-hand thumb rule- When the thumb of the right hand is placed in the direction of the current. In a current-carrying wire the direction of curved fingers will give the direction of the magnetic field due to the conducting wire.
- Clock Rule – For a current-carrying coil, if fingers of the right hand are curved in the direction of current stretched Thumb will give the direction of the magnetic field due to.

## Magnetic Field For A Current Carrying Coil On Its Axis –

Consider a circular coin of radius capital r in which current ‘I’ is flowing. we are to find the magnetic field at a point P which is at a distance x from the centre on the axis of a coil for which we consider an element DL the distance of deer from point P is r. The angle made between DL and r is 90 degree. Magnetic field due to this element on point P is is DB, r makes an angle with the vertical. So there are two components of magnetic field DB. One component is horizontal component and another is vertical component. Vertical components of magnetic field are equal in magnitude but opposite in direction so vertical component gets cancelled resultant magnetic field is found due to only e horizontal component. So result 10th will be horizontal component.

### Variation Of Magnetic Field And X –

In the variation graph of the magnetic field with the distance x from the center magnetic field is maximum at the center and as a distance increase value of B decreases in the graph. There are two points P1 and P2 where x is equal to half of R at the radius of this point of curvature is zero and size of curvature changes at this point that’s why these are called the point of inflection.