Physics : Magnetism and Magnetic Effects of Electric Current

Definition and explanation of Biot- Savart law

Biot and Savart experimentally observed that the magnitude of magnetic field *d* at a point P (Figure 3.37) at a distance r from the small elemental length taken on a conductor carrying current varies

i.directly as the strength of the current I

ii.directly as the magnitude of the length element

iii.directly as the sine of the angle (say,Î¸) between and *r* *^* .

iv.inversely as the square of the distance between the point P and length element .

This is expressed as

in SI units and k = 1 in CGS units. In vector notation,

Here vector *d* is perpendicular to both I (pointing the direction of current flow) and the unit vector *r* *^* directed from toward point P (Figure 3.38).

The equation (3.37) is used to compute the magnetic field only due to a small elemental length d*l* of the conductor. The net magnetic field at P due to the conductor is obtained from principle of superposition by considering the contribution from all current elements I . Hence integrating equation (3.37), we get

where the integral is taken over the entire current distribution.

Cases

1. If the point P lies on the conductor, then Î¸ = 0Âº. Therefore, *d * is zero.

2. If the point lies perpendicular to the conductor, then Î¸ = 90Âº. Therefore, *d *

Similarities between Coulombâ€™s law and Biot-Savortâ€™s law

Electric and magnetic fields

Â· obey inverse square law, so they are long range fields.

Â· obey the principle of superposition and are linear with respect to source. In magnitude,

Note that the exponent of charge q (source) and exponent of electric field E is unity. Similarly, the exponent of current element Id*l* (source) and exponent of magnetic field B is unity. In other words, electric field is proportional only to charge (source) and not on higher powers of charge ( *q*2 , *q*3 , *etc*). Similarly, magnetic field is proportional to current element *I* (source) and not on square or cube or higher powers of current element. The cause and effect have linear relationship.

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12th Physics : Magnetism and Magnetic Effects of Electric Current : Definition and explanation of Biot- Savart law |

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