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Download eSaral App**Magnetic field due to long straight conductor**

Here we will discuss all the cases involved in magnetic field due to Conductor such as Magnetic Field due to Infinite Straight Conductor, and many more discussed below:

Consider a long straight conductor XY through which current I is flowing from $X$ to Y. Let $P$ be the observation point at a distance ‘r’ ‘from the conductor XY. Let us consider an infinitesimally small current element $\mathrm{CD}$ of length d\ell. Let s be the distance of $\mathrm{P}$ from the mid-point $\odot$ of the current element. Let $\theta$ be the angle which OP makes with the direction of current. The magnetic field at $P$ due to the current element $C D$ is $\mathrm{dB}=\frac{\mu_{0}}{4 \pi} \frac{\mathrm{Id} \ell \sin \theta}{\mathrm{s}^{2}}[\text { Biot-Savart’s law }]$

The magnetic field at P due to the whole of the conductor XY

**Case I :**

If the conductor is infinitely long, then $\theta_{1}=90^{\circ}$ and $\theta_{2}=90^{\circ}$

$\mathrm{B}=\frac{\mu_{0} \mathrm{I}}{4 \pi}\left[\sin \frac{\pi}{2}+\sin \left(\frac{\pi}{2}\right)\right]=\frac{\mu_{0} \mathrm{I}}{4 \pi \mathrm{r}}[1+1]=\frac{\mu_{0}}{4 \pi} \frac{2 \mathrm{I}}{\mathrm{r}}$

Or

**Case II : **If conductor is of infinite length but one end is in front of point $P$ i.e. one end of conductor starts from point $N$ then $\theta_{1}=0^{\circ}$ and $\theta_{2}=90^{\circ}$

**Case III :**

Conductor is finite length and point P is just in front of middle of the conductor

**Case IV :**

**Also Read:**

**Click here for the Video tutorials of Magnetic Effect of Current Class 12**

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