biot-savart law form

Question

Differential magnetic field dB due to current element Idl at position vector r (angle θ)?

RankGuru · Accepted Answer

1. **Biot-Savart Law (Vector Form)**: $d\vec{B} = \frac{\mu_0}{4\pi} \frac{I (d\vec{l} 	imes \hat{r})}{r^2}$.
2. **Magnitude Extraction**: Using the definition of a cross product ($|A 	imes B| = AB \sin 	heta$):
   - $|d\vec{l} 	imes \hat{r}| = dl 	imes 1 	imes \sin 	heta$.
3. **Resulting Magnitude**: $dB = \frac{\mu_0}{4\pi} \frac{I \, dl \sin 	heta}{r^2}$.
4. **Conclusion**: The differential magnetic field follows an inverse square law and depends on the sine of the angle between the current element and the position vector.

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biot-savart law form

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