Question

An infinitely long straight conductor is bent into the shape as shown in figure. It carries a current i A and radius of the circular loop is rm, The magnetic field at the centre of the loop is :

• A. $ {{\mu }_{0}}i(\pi -1)/2\pi r $
• B. $ {{\mu }_{0}}i(\pi +1)/2\pi r $
• C. $ {{\mu }_{i}}/2\pi r $
• D. none of the above

Answer 1

Answer: (A)

According to the question, the magnetic field due to straight part of the conductor at the contre is given by $ =\frac{{{\mu }_{0}}i}{2\pi r} $ Now the magnetic field due to a circular part of wire at the centre $ =\frac{{{\mu }_{0}}i}{2r} $ These two fields are in opposite direction. Therefore, net field $ =\frac{{{\mu }_{0}}i}{2r}-\frac{{{\mu }_{0}}i}{2\pi r}=\frac{{{\mu }_{0}}i}{2\pi r}(\pi -1) $