Question

Two circular current carrying coils of radii $3cm$ and $6cm$ are each equivalent to a magnetic dipole having equal magnetic moments. The currents through the coils are in the ratio of __

• A. $\sqrt{2}:1$
• B. $2:1$
• C. $2\sqrt{2}:1$
• D. $4:1$

Answer 1

The correct option is D $4:1$

Given: $r_1=$3 cm ,$r_2=$6 cm

Solution: By using formula of current carrying loop in magnetic field

M=iA

Here M is equal according to the question

So,$i_1{A}_1=i_2{A}_2$

$\frac{i_1}{i_2}=\frac{A_2}{A_1}$

$\frac{i_1}{i_2}=\frac{r_2^2}{r_1^2}$

$\frac{i_1}{i_2}=\frac{6^2}{3^2}$

Hence the correct option is D