Complete Question
The complete question is shown on the first uploaded image
Answer:
The formula for mutual inductance of two concentric loops [tex]M = \frac{\pi a^2 \mu_0}{2R}[/tex]
Explanation:
Generally magnetic field in a concentric coplanar loop  is mathematically represented as
         [tex]B = \frac{\mu_0 I_b}{2R}[/tex]
     Where [tex]\mu_o[/tex] is the permeability o free space
           R is the radius
          [tex]I_b[/tex] is the current
The magnetic flux  of two concentric loops is mathematically represented as
       [tex]\O = \frac{\mu_o I_b}{2R} * \pi a^2[/tex]
         [tex]= \frac{\pi a^2 \mu_o}{2R} * I_b[/tex]
   a is the area
Generally magnetic inductance is mathematically represented as
        [tex]M = \frac{\O }{I_b}[/tex]
Substituting for  [tex]\O[/tex] in the above equation
       [tex]M = \frac{\pi a^2 \mu_0}{2R}[/tex]
       Â
