Name: Right Hand Thumb Rule
Uploaded: 2019-07-19
Duration: 3 min 25 s
Description: When electricity (conventional current) flows in a long straight wire, it creates a circular or cylindrical magnetic field around the wire according to the r...

Question

State Biot-Savart&rsquo;s law for the magnetic field due to a current-carrying element, explaining the symbols. Define &lsquo;tesla&rsquo; on the basis of this law. How is gauss related to tesla?

Accepted Answer

Biot -Savart’s law:According to this law the magnetic field $\vec{dB}$ , due to current carrying element $\vec{dl}$ depend upon.

(i) $\vec{d B}$ is proportional to current $I$ flowing though $dl i.e .$ $\vec{dB} \propto I$

(ii) $\vec{dB}$ is proportional to the length of $dl$ i.e. $\vec{d B} \propto dl$

(iii) $\vec{dB}$ is proportional to sine of angle between current element and position vector( of angle $θ$ )between $I \vec{dl}$ & $\vec{r}$ i.e. $\vec{dB} \propto \sin θ$

(iv) $\vec{dB}$ is inversely proportional to the square of distance $r$ , between element and point $P$

where $dB$ is being calculated i.e. $\vec{dB} \propto \frac{1}{r^{2}}$

By combining all above relations

$\vec{dB} \propto \frac{I dl \sin θ}{r^{2}}$

$\Rightarrow \vec{dB} = \frac{μ_{0}}{4 π} \frac{I dl sinθ}{r^{2}} [μ_{0} = permeability in free space]$

$\Rightarrow \vec{d B} = \frac{μ_{0}}{4 π} I (\frac{\vec{d l} \times \hat{r}}{r^{2}}) and \vec{d B} = \frac{μ_{0}}{4 π} I (\frac{\vec{d l} \times \vec{r}}{r^{3}})$

(ii) Tesla (T): $1$ Tesla is the $10^{- 7}$ times the magnetic field produced by the conductor of length $1 m$ coming $1 A$ Current at a distance of $1 m$ perpendicular to the axis of conductor.

(iii) $1 T = 10^{4}$ Gauss.

State Biot-Savart’s law for the magnetic field due to a current-carrying element, explaining the symbols. Define ‘tesla’ on the basis of this law. How is gauss related to tesla?

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