Question

Two circular coils are made of two identical wires of the same length. If the number of turns of the two coils are $4$ and $2$, then the ratio of the magnetic inductions at the centre will be :

• A. $4:1$
  
• B. $2:1$
  
• C. $1:2$
  
• D. $1:1$
  

Answer 1

The correct option is A $4:1$

since length is same

$4\left(r^{\prime }\right)=2\left(r\right)$, r' and r are the radii of the coils after winding the turns.

$B=\frac{{\mu }_{0}ni}{2r}$

$B_1=\frac{{\mu }_{0}4i}{2r^{\prime }}$

$B_2=\frac{{\mu }_{0}2i}{2r}=\frac{{\mu }_{0}2i}{2\left(2r^{\prime }\right)}=\frac{{\mu }_{0}i}{2r^{\prime }}$

$\therefore B_1:B_2=4:1$