question_answer

A straight conductor carrying a current I splits into two identical semicircular arcs as shown in figure below. What is the magnitude of the magnetic field at the centre C of the resulting circular arcs of radius R?

A)  0                                            

B)  \[\frac{{{\mu }_{0}}l}{4R}\]    

C)  \[\frac{{{\mu }_{0}}l}{2R}\]                        

D)  \[\frac{{{\mu }_{0}}l}{R}\]

Correct Answer: A

Solution :

Magnetic field due to BAC arc is \[B=\frac{{{\mu }_{0}}\pi (I/2)}{4\pi R}\otimes \]                              ... (i) Magnetic field due to ADC arc is \[B=\frac{{{\mu }_{0}}\pi (I/2)}{4\pi R}\]                                               ? (ii) From Eqs. (i) and (ii) net magnetic field is zero.