Question: 28: Given below are two statements
Statement 1 : Biot-Savart’s law gives us 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 produce 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
(1) Statement I is correct and Statement II is incorrect
(2) Statement I is incorrect and Statement II is correct
(3) Both Statement I and Statement II are correct
(4) Both Statement I and Statement II are incorrect
Answer: Option (1)
Explanation:
Biot-Savart’s law gives the magnetic field produced by an infinitesimal current
element of a current-carrying conductor.
The law is written as
d\vec{B} = \frac{\mu_0}{4\pi}\frac{I\, d\vec{l} \times \hat{r}}{r^2}This clearly shows that Biot-Savart’s law applies to an infinitesimal current element I\,d\vec{l}. Hence, Statement I is correct.
Coulomb’s law gives the electric field due to a point charge and is written as
\vec{E} = \frac{1}{4\pi\varepsilon_0}\frac{q}{r^2}\hat{r}Here, the charge q is a scalar quantity, whereas the current element I\,d\vec{l} is a vector quantity.
Statement II incorrectly states that Biot-Savart’s law involves a scalar source and Coulomb’s law involves a vector source, which is opposite to the actual physical meaning.
Therefore, Statement II is incorrect.
Hence, the correct answer is Option (1).