Question

A long straight conductor, carrying a current I, is bent into the shape shown in the figure. The radius of the circular loop is r. The magnetic field at the centre of the loop is

• A. $\frac{{\mu }_{0}i}{2r}[1+\frac{1}{\pi }]$ into the page
  
• B. $\frac{{\mu }_{0}i}{2r}[1-\frac{1}{\pi }]$ out of the page
  
• C. $\frac{{\mu }_{0}i}{2r}[1-\frac{1}{\pi }]$ into the page
  
• D. $\frac{{\mu }_{0}i}{2r}[1+\frac{1}{\pi }]$ out of the page

Answer 1

The correct option is C $\frac{{\mu }_{0}i}{2r}[1-\frac{1}{\pi }]$ into the page


$B_1=\frac{{\mu }_{0}i}{2r}$ for Circular loop $\theta$
$B_2=\frac{{\mu }_{0}i}{2\pi r}$ for straight wire
$B=B_1-B_2=\frac{{\mu }_{0}i}{2r}[1-\frac{1}{\pi }]$ in to the page