Question: Q. 1. (i) State Biot-Savart’s law in vector form expressing the magnetic field due to an element $\overrightarrow{d l}$ carrying current $I$ at a distance $r$ from the element.
(ii) Write the expression for the magnitude of the magnetic field at the centre of a circular loop of radius $r$ carrying a steady current $I$. Draw the field lines due to the current loop.
U] [O.D. Comptt. I, II, III 2014]
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Solution:
Ans. (i) According to Biot-Savart’s law, the magnetic field due to a current element $\overrightarrow{d l}$ carrying current $I$ at a point $P$ with position vector $\vec{r}$ is given by
$$ d \vec{B}=\frac{\mu_{0}}{4 \pi} I\left(\frac{\overrightarrow{d l} \times \vec{r}}{r^{3}}\right) $$
(ii)
$$ B=\frac{\mu_{0} I}{2 r} $$
Field lines :
