question_answer

The wire shown in the figure given below, carries a current of 10 A. Determine the magnitude of the magnetic field at the centre O. Given, radius of the bent coil is 3 cm.

 

Answer:

Given, r = 3 cm \[=3\times {{10}^{-2}}m,\] i = 10 A From the given figure, Angle made by the circular arc at the point O, \[\theta =360{}^\circ -90{}^\circ =270{}^\circ \] or \[\frac{3}{2}\pi \] Since, we know that, magnetic field at the centre of a current carrying arc, \[B=\frac{{{\mu }_{0}}}{2}\times \frac{i}{r'}\times \frac{\theta }{2\pi }\] \[=\frac{4\pi \times {{10}^{-7}}}{2}\times \frac{10}{3\times {{10}^{-2}}}\times \frac{3\pi /2}{2\pi }=1.57\times {{10}^{-4}}T\]