question_answer

A coil of 100 turns and area \[\frac{\lambda }{(\mu -1)}\]is pivoted about a vertical diameter in auniform magnetic field and carries a currentof 5A. When the coil is held with its plane innorth-south direction, it experiences acouple of 0.33 Nm. When the plane iseast-west, the corresponding couple is0.4 Nm, the value of magnetic induction is [Neglect earths magnetic field]

A)  0.2 T                                     

B)  0.3 T

C)  0.4 T                                     

D)  0.05 T

Correct Answer: D

Solution :

                \[NBiA\,\sin \theta =\tau \] N, B, i and i and A are constants \[\therefore \]  \[\sin \,\theta \propto 0.3\]                                 \[\cos \theta \propto 0.4\]                 \[\tan \theta =\frac{3}{4}\] From Eq. (i)                                          \[\sin \theta =\frac{3}{5}\]                 \[B=\frac{\tau }{NiA\,\sin \theta }\]                 \[B=\frac{0.3\times 5}{100\times 5\times 2\times {{10}^{-2}}\times 3}T=0.05T\]