Short Question Answers

Q1. State and explain Biot-Savart law.

Ans. Statement: According to Biot-Savart’s law, the magnitude of the magnetic field $dB$ is proportional to the current $i$,  $sine$ angle between $r$ and $dl$ , the element length $dl$,and inversely proportional to the square of the distance $r$.

Explanation: A finite conductor $XY$ carrying current i consider an infinitesimal element dl of the conductor. The magnetic field $dB$ due to this element is to be determined at a point $p$ which is at a distance $r$ from it. Let $θ$ be the angle between $dl$ and the position vector $r$.

$$ dB \propto i $$$$dB \propto dl $$$$dB \propto sin \theta $$$$ dB \propto\frac 1{r^{2}}$$ $$dB \propto\frac{idlsin\theta}{r^2}$$$$\therefore dB= \frac {\mu _{0}}{4\pi }\frac {idlsin\theta }{r^{2}}$$

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Q2. State and explain Biot-Savart law.