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 $=\frac{{\mu }_{0}i}{2r}-\frac{{\mu }_{0}i}{2\pi r}=\frac{{\mu }_{0}i}{2\pi r}(\pi -1)$