## Moving charges and magnetism

# Biot-Savart Law

- According to Biot savarts law the magnitude of the intensity of magnetic field due to a smell element “dl” is \tt dB = \frac{\mu_{o}}{4 \pi } \frac{i d l \sin \theta}{r^{2}}
- The magnetic field due to entire conductor is given by \tt B = \frac{\mu_{o}}{4 \pi} \int \frac{d l \sin \theta}{r^{2}}
- The magnetic field at a point on the axis of coil when \tt B = \frac{\mu_{o} n i r^{2}}{2 (r^{2} + x^{2})^{3/2}} where, r = radius x = distance
- The magnetic field on the axis of the coil when π >>>> r\tt B = \frac{\mu_{o} n i r^{2}}{2 x^{3}} = \frac{\mu_{o}}{4 \pi} \left(\frac{2 n i \pi r^{2}}{x^{3}}\right)
- If current in the loop is anti-clock wise it acts as a North Pole
- If current in the loop is clock wise it acts as a South Pole

### View the Topic in this video From 29:29 To 40:33

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1. Biot-Savart Law

|d\overrightarrow{B}| = \frac{\mu_{0}}{4 \pi}\frac{Idl \sin \theta}{r^{2}}

2. If the circular loop has *N* turns then magnetic field strength at its centre is B = \frac{\mu_{0}NI}{2r} and at any point on the axis of circular loop is B = \frac{\mu_{0}Nlr^{2}}{2(r^{2} + x^{2})^{3/2}}