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  • A coil of one turn is made of a wire of certain length and then from the same length a coil of two turns is made. If the same current is passed in both the cases, then the ratio of the magnetic ind

A coil of one turn is made of a wire of certain length and then from the same length a coil of two turns is made. If the same current is passed in both the cases, then the ratio of the magnetic inductions at their centres will be

Option: 1

2:1


Option: 2

1:4


Option: 3

4:1


Option: 4

1:2


Answers (1)

best_answer

Let

be length of wire.
Ist case :
\mathrm{=2 \pi r \Rightarrow \mathrm{r}=\frac{\ell}{2 \pi}}
\mathrm{B}=\frac{\mu_0 \mathrm{In}}{2 \mathrm{r}}=\frac{\mu_0 \mathrm{I} \times 2 \pi}{2 \mathrm{l}}=\frac{\mu_0 \pi \mathrm{I}}{\ell}[\because n=1] ............(1)

2nd Case   \mathrm{ : \ell=2\left(2 \pi r^{\prime}\right) \Rightarrow r^{\prime}=\frac{1}{4 \pi} }

\mathrm{ \mathrm{B}^{\prime}=\frac{\mu_0 \mathrm{In}}{2 \frac{1}{4 \pi}}=\frac{2 \mu_0 \mathrm{I} \pi}{\frac{\ell}{2}}=4\left(\frac{\mu_0 \pi \mathrm{I}}{1}\right)=4 \mathrm{~B}, \\ }
  using (1) (where n=2)
 

Posted by

rishi.raj

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