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Discussion Forum



1)

The figure shows the circular coil carrying current l kept very close but not touching at a point  A on a straight conductor carrying the same current l. The magnitude of magnetic induction  at the centre of the circular coil will be 

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A) $\frac{\mu_{0}l}{2r}(1+\frac{1}{\pi})$

B) $\frac{\mu_{0}l}{2\pi r}$

C) $\frac{\mu_{0}l}{2 r}$

D) zero

E) None of these

Answer:

Option E

Explanation:

 Magnetic  induction at the centre of circular current carrying loop.

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$B_{1}=\frac{\mu_{0}i}{2r}$              (downward direction )

 Magnetic induction at the centre O due to straight  wire,

$B_{2}=\frac{\mu_{0}}{2\pi}\frac{i}{r}$   (upward direction)

 Net magnetic induction at O,

 $B=B_{1}-B_{2}=\frac{\mu_{0}i}{2r}-\frac{\mu_{0}}{2\pi}.\frac{i}{r}$

 $=\frac{\mu_{0}i}{2r}\left[1-\frac{1}{\pi}\right]$  [ downward direction]

 Hence, there are no option correct.