| Direction: Q.21 to Q.25 |
| 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 calculus problem when the distance from the current to the field point is continuously chaning. |
| According to this 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 \[dB=\frac{{{\mu }_{0}}}{4\pi }\frac{I(d\,\overrightarrow{l}\times \overrightarrow{r})}{{{r}^{3}}}\]. |
| Biot-Savart law has certain similarities as well as difference with Coloumb's law for electrostatic field e. g., there is an angle dependence in Biot-Savart law which is not present in electrostatic case. |
| Read the given passage carefully and give the answer of the following questions. |
A) of position vector \[\overrightarrow{r}\] of the point
B) of current element \[d\text{ }\overrightarrow{l}\]
C) perpendicular to both \[d\text{ }\overrightarrow{\text{l}}\] and \[\overrightarrow{r}\]
D) perpendicular to \[d\text{ }\overrightarrow{\text{l}}\] only
Correct Answer: C
Solution :
(c) perpendicular to both \[d\text{ \vec{l}}\] and\[\vec{r}\] 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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