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)  \[{{0}^{o}}\]            

B)  \[{{90}^{o}}\]

C)  \[{{180}^{o}}\]         

D)  \[{{45}^{o}}\]

Correct Answer: B

Solution :

From Biot-Savart's law, the magnetic field \[d\vec{B}\] 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 \[\vec{l}\] and \[\vec{r}\]. Maximum value of sin \[\theta =1,\]when \[\theta ={{90}^{o}}\]. Hence, for magnetic field to be maximum the angle is \[{{90}^{o}}\].