A small conducting loop of radius o and resistance r is pulled wi… - Vidyadip

MCQ

A small conducting loop of radius $o$ and resistance $r$ is pulled with velocity $v$ perpendicular to a long straight conductor carrying a current $i_o$ . If a constant power $P$ is dissipated in the loop. The variation of velocity of the loop as a function of $x$ .Given that $x >> 0$

✓
$ \frac{2x^2}{\mu_0 i_0 a^2}\sqrt{Pr}$
B
$ \frac{4x^2}{\mu_0 i_0 a^2}\sqrt{Pr}$
C
$ \frac{6x^2}{\mu_0 i_0 a^2}\sqrt{Pr}$
D
none of these

✓

Answer

Correct option: A.

$ \frac{2x^2}{\mu_0 i_0 a^2}\sqrt{Pr}$

a
$\mathrm{B}=\frac{\mu_{0} \mathrm{i}}{2 \mathrm{x}}$

$\phi=\frac{\mu_{0} \mathrm{i}}{2 \mathrm{x}}\left(\pi \mathrm{a}^{2}\right)$ ........$(1)$

$\varepsilon=\frac{\mathrm{d} \phi}{\mathrm{dt}}=\frac{\mu_{0} \mathrm{i}\left(\pi \mathrm{a}^{2}\right)}{2}\left(\frac{-1}{\mathrm{x}^{2}}\right)(\mathrm{v})$ .........$(2)$

$\mathrm{i}=\frac{\mu_{0} i_{0} \pi \mathrm{a}^{2} \mathrm{v}}{\mathrm{r} \mathrm{x}^{2}}$ ..........$(3)$

$\mathrm{P}=\mathrm{i}^{2} \mathrm{r}$ ..........$(4)$

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