Magnetic Field Due To A Current Element Biot Savart Law

Let's evaluate the given statements about Biot-Savart's law and determine their correctness:

Statement I: Biot-Savart's law gives an expression for the magnetic field strength due to an infinitesimal current element of a current-carrying conductor only.

This statement is correct. Biot-Savart's law describes how the magnetic field ( ) is generated by a small segment of a current-carrying wire. The magnetic field produced by an infinitesimal current element is given by:

where is the current, is the vector length of the infinitesimal segment, is the unit vector from the element to the point where the field is measured, and is the distance between the element and the point in question. This expression is specific to current elements.

Statement II: Biot-Savart's law is analogous to Coulomb's inverse square law of charge , with the former being related to the field produced by a scalar source, , while the latter being produced by a vector source, .

This statement is incorrect. Biot-Savart's law and Coulomb's law are analogous in that they both involve inverse-square relationships for fields produced by charge or current elements. However, in Biot-Savart's law, the current element is a vector quantity, not a scalar. In contrast, the electric field in Coulomb’s law is produced by a scalar charge .

Conclusion: Considering the analysis above, the most appropriate answer is: