The correct Biot-Savart law in vector form is
- $d \vec{B} = \frac{\mu_{0}}{4 \pi} \frac{I\left(d \vec{l} \times \vec{r} \right)}{r^{2}} $
- $d \, \vec{B} = \frac{\mu_{0}}{4 \pi} \frac{I\left(d \vec{l} \times \vec{r} \right)}{r^{3}}$
- $d \, \vec{B} = \frac{\mu_{0}}{4 \pi} \frac{I d \vec{l} }{r^{2}} $
- $d \, \vec{B} = \frac{\mu_{0}}{4 \pi} \frac{I d \vec{l} }{r^{3}} $
The Correct Option is B
Solution and Explanation
$\overrightarrow{dB} = \frac{\mu_{0}}{4\pi} \frac{I \overrightarrow{dl} \times\vec{r}}{r^{3}} $
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Concepts Used:
Biot Savart Law
Biot-Savart’s law is an equation that gives the magnetic field produced due to a current-carrying segment. This segment is taken as a vector quantity known as the current element. In other words, Biot-Savart Law states that if a current carrying conductor of length dl produces a magnetic field dB, the force on another similar current-carrying conductor depends upon the size, orientation and length of the first current carrying element.
The equation of Biot-Savart law is given by,
\(dB = \frac{\mu_0}{4\pi} \frac{Idl sin \theta}{r^2}\)
Application of Biot Savart law
- Biot Savart law is used to evaluate magnetic response at the molecular or atomic level.
- It is used to assess the velocity in aerodynamic theory induced by the vortex line.
Importance of Biot-Savart Law
- Biot-Savart Law is exactly similar to Coulomb's law in electrostatics.
- Biot-Savart Law is relevant for very small conductors to carry current,
- For symmetrical current distribution, Biot-Savart Law is applicable.
For detailed derivation on Biot Savart Law, read more.