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,θ) 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 θ = 0º. Therefore, *d * is zero.

2. If the point lies perpendicular to the conductor, then θ = 90º. Therefore, *d *

Similarities between Coulomb’s law and Biot-Savort’s law

Electric and magnetic fields

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

· 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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