| Directions : (26-30) |
| Biot - Savart Low |
| A magnetic field can be produced by moving, charges or electric currents. The basic equation governing the magnetic field due to a current distribution is the Biot-Savart Law. |
| Finding the magnetic field resulting from a current distribution involves the vector product, and is inherently a calculas problem when the distance from the current to the field point is continuously changing. |
| According to the law, the magnetic field at a point due to a current element of length \[d\,\overrightarrow{l}\] carrying current I, at a distance r from the element is \[dB=\frac{{{\mu }_{0}}}{4\pi }\frac{I\left( d\overrightarrow{l}\times \overrightarrow{r} \right)}{{{r}^{3}}}\]. |
| Biot-Savan law has certain similartities as well as difference with Coloumb's law for electrostatic field e.g., there is an angle dependence on Biot-Savart law which is not present in electrostatic case. |
A) of position vector \[\overrightarrow{r}\] of the point
B) of current element \[d\overrightarrow{l}\]
C) perpendicular to both \[d\overrightarrow{l}\]and \[\overrightarrow{r}\]
D) perpendicular to dl only
Correct Answer: C
Solution :
According to Biot-Savart's law, the magnetic induction due to a current element is given by \[d\overrightarrow{B}=\frac{{{\mu }_{0}}}{4\pi }\frac{Id\overrightarrow{l}\times \overrightarrow{r}}{{{r}^{3}}}\] This is perpendicular to both \[d\overrightarrow{l}\]and \[\overrightarrow{r}\].
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