KVPY SX SB Exam 2015 Question Paper

Question : 38 of 120

Marks: +1, -0

A wire bent in the shape of a regular n-polygonal loop carries a steady current I. Let

l

be the perpendicular distance of a given segment and R be the distance of vertex both from the centre of the loop. The magnitude of the magnetic field at the centre of the loop is given by -

${ n µ_0I} /{2πl}\sin (π/n)$
${ n µ_0I} /{2πR}\sin (π/n)$
${ n µ_0I} /{2πl}\coc (π/n)$
${ n µ_0I} /{2πR}\coc (π/n)$

Validate

Solution:

n sides, n wires

θ_1 = θ_2 =π/n

_\net

at centre = n × B due to one side

B_\net={n×µ_0I}/{4πl}[\sinθ_1 + \sin θ_2]

⇒

{nµ_0I}/{2πl}\sinπ/n

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