Question

Given below are two statements
Statement I: Biot-Savart's law gives on the expression for the magnetic field strength of an infinitesimal current element (Idl) of a current carrying conductor only.
Statement II: Biot-Savart’s law is analogous to Coulomb's inverse square law of charge q, with the former being related to the field produced by a scalar source, Idl while the latter being produced by a vector source, q.
In light of above statements choose the most appropriate answer from the options given below:

• A. Both Statement I and Statement II are correct
• B. Both Statement I and Statement II are incorrect
• C. Statement I is correct and Statement II is incorrect
• D. Statement I is incorrect and Statement II is correct

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Biot-Savart's Law and Coulomb's Law are fundamental laws describing the fields produced by their respective sources (current elements for magnetic fields and static charges for electric fields).
They both follow an inverse-square relationship with distance.
Step 2: Detailed Explanation:
Statement I analysis:
Biot-Savart's law provides the mathematical description of the magnetic field \(d\vec{B}\) produced by an infinitesimal current element \(Id\vec{l}\).
The formula is:
\[ d\vec{B} = \frac{\mu_0}{4\pi} \frac{I(d\vec{l} \times \hat{r})}{r^2} \]
This law is specifically defined for these small elements; to find the total field of a whole wire, we must integrate these individual contributions.
Hence, Statement I is correct.

Statement II analysis:
In Biot-Savart's law, the source is the current element \(Id\vec{l}\).
A current element has both a magnitude and a specific direction, making it a vector source.
In Coulomb's law, the source is the electric charge \(q\).
Electric charge is a physical property that does not have direction, making it a scalar source.
Statement II incorrectly swaps these definitions by calling \(Idl\) a scalar source and \(q\) a vector source.
Hence, Statement II is incorrect.
Step 3: Final Answer:
Statement I is correct and Statement II is incorrect.