Two circular coils are made from a uniform copper wire. Radii of circular coils is in the ratio 3:4 and number of turns in the ratio 3:5. If they are connected in series across a battery.
Statement (A) : Ratio between magnetic field inductions at their centers is 4 : 5
Statement (B) : Ratio between effective magnetic moments of the two coils is 16 : 15

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Both statements are wrong

Both statements are correct

Statement A alone is correct

Statement B alone is correct

answer is C.

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Detailed Solution

a) $B = \frac{μ_{0} ni}{2 r}; \frac{B_{1}}{B_{2}} = (\frac{n_{1}}{n_{2}}) (\frac{r_{2}}{r_{1}})$
$\frac{B_{1}}{B_{2}} = \frac{3}{5} \times \frac{4}{3}; \frac{B_{1}}{B_{2}} = 4 : 5$
b) M = niA
$\frac{M_{1}}{M_{2}} = (\frac{n_{1}}{n_{2}}) {(\frac{r_{1}}{r_{2}})}^{2}; = (\frac{3}{5}) (\frac{9}{16}) = \frac{27}{80}$
statement A alone is correct.