Question

What is K in magnetic field?

Answer 1

1. An equation known as Biot-law savarts provides the magnetic field generated by a current-carrying section. This section is considered to be the current element, a vector quantity.
2. Consider a current-carrying wire $\text{'}i\text{'}$ in a specific direction as shown in the above figure. Take a small element of the wire of length $\mathrm{ds}$.
3. The direction of this element is along that of the current so that it forms vector $ids$.
4. To know the magnetic field produced at a point due to this small element, one can apply Biot-Savart’s Law.
5. Let the position vector of the point in question drawn from the current element be $\mathrm{r}$ and the angle between the two be $\mathrm{\theta }$.
6. The Biot Savart Law is used to determine the magnetic field created at a spot due to the little current element indicated in the illustration.
7. The equation of the magnetic field is written as:
   $\mathrm{dB}=\mathrm{k}\frac{\mathrm{Ids}\times \hat{\mathrm{r}}}{{\mathrm{r}}^2}$
   Where $dB$is the magnetic field, $\mathrm{I}$ is the current in the wire, $\mathrm{ds}$ is the element of length,the position vector of the point in question drawn from the current element be $\mathrm{r}$ and the angle between the two be $\mathrm{\theta }$.
8. $k$ is the magnetic constant and its value is given as:
   $$\begin{gathered} \mathrm{k}=\frac{{\mathrm{\mu }}_0}{4\mathrm{\pi }}where{\mathrm{\mu }}_0\mathrm{is}permeabilityoffreespace \\ \mathrm{k}=\frac{4\mathrm{\pi }\times {10}^{-7}H/m}{4\mathrm{\pi }} \\ \mathrm{k}={10}^{-7}\mathrm{H}/\mathrm{m} \end{gathered}$$