question_answer

For the magnetic field to be maximum due to a small element of current carrying conductor at a point, the angle between the element and the line joining the element to the given point must be :

A) \[0{}^\circ \]

B) \[90{}^\circ \]

C) \[180{}^\circ \]

D) \[45{}^\circ \]

Correct Answer: B

Solution :

                 From Biot-Savarts law, the magnetic field d B at P due to the current element\[idl\]is given by \[dB=\frac{{{\mu }_{0}}}{4\pi }\frac{idl\sin \theta }{{{r}^{2}}}\] where\[\theta \]is angle between id\[\overrightarrow{l}\]and\[\overrightarrow{r}\]Maximum value of\[sin\text{ }\theta =1,\]when\[\theta ={{90}^{o}}\]. Hence, for magnetic field to be maximum the angle is\[{{90}^{o}}\].