question_answer

Current through ABC and \[ABC\]is\[I\]. What is the magnetic field at P? BP = PB = r   (Here C B PBC are collinear)

A)  \[B=\frac{1}{4\pi }\frac{2I}{r}\]                

B)  \[B=\frac{{{\mu }_{0}}}{4\pi }\left( \frac{2I}{r} \right)\]

C)  \[B=\frac{{{\mu }_{0}}}{4\pi }\left( \frac{I}{r} \right)\]                  

D)  zero

Correct Answer: B

Solution :

                 The magnetic field at P would be given by \[{{B}_{net}}={{B}_{BP}}-{{B}_{BP}}=\frac{{{\mu }_{0}}I}{4\pi r}-\left( -\frac{{{\mu }_{0}}I}{4\pi r} \right)\] \[=2\left( \frac{{{\mu }_{0}}}{4\pi }\frac{I}{r} \right)=\frac{{{\mu }_{0}}}{4\pi }\frac{2I}{r}\]