A) \[\frac{5}{16},\] but out of the plane of the paper
B) \[\frac{5}{16},\] but into the plane of the paper
C) \[\frac{7}{16},\] but out of the plane of the paper
D) \[\frac{7}{16},\] but into the plane of the paper
Correct Answer: D
Solution :
(i) Magnetic field at the centre due to the curved portion \[DA=\frac{{{\mu }_{0}}i}{4\pi R}\left( \frac{3\pi }{2} \right)\] According to right hand screw rule, the magnetic field will be into the plane of paper. (ii) Magnetic field at M due to AB is zero. (iii) Magnetic field at the centre due to the curved portion BC is \[\frac{{{\mu }_{0}}i}{4\pi 2R}\left( \frac{\pi }{2} \right)\]. According to right hand screw rule, the magnetic field will be into the plane of paper. (iv) Magnetic field at M due to DC is zero. Hence, the resultant magnetic field at M \[=\frac{3{{\mu }_{0}}i}{8R}+0+\frac{{{\mu }_{0}}i}{16R}+0=\frac{7{{\mu }_{0}}i}{16R}\]You need to login to perform this action.
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