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In Fig. infinite conducting rings each h...

In Fig. infinite conducting rings each having current i in the direciton shown are placed concentrically in the same plane as shown in the figure. The radii of rings are `r,2r,2^2r,2^3r,......,(oo)`. The magnetic field at the centre of rings will be

A

Zero

B

`(mu_(0)i)/(r)`

C

`(mu_(0)i)/(2r)`

D

`(mu_(0)i)/(3r)`

Text Solution

Verified by Experts

The correct Answer is:
D
`B=(mu_(0)i)/(2r)-(mu_(0)i)/(2(2r))+(mu_(0)i)/(2(2^(2)r))...(oo)`
`B=(mu_(0)i)/(2r) [1-1/2+1/(2^(2))-(1)/(2^3)+oo]`
`B=(mu_(0)i)/(2r)[(1)/(1-(-(1)/(2)))] implies B=(mu_(0)i)/(3r)`.
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