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Question

Magnetic field at P due to given structure is
1266425_c58fb0b95f194919bb85ea405441a6a5.png

A
(μ4π)Iθ2R
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B
μ4π2Iθ5R
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C
(μ4π)5Iθ6R
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D
(μ4π)2Iθ6R
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Solution

The correct option is C (μ4π)5Iθ6R
Given: Current=i
Solution:Magnetic field due to the structure at P is given by:
Bp=B1+B2+B3+B4+B5

But, B2,B4=0( angle subtend by straight current carrying conductor is zero)

Bp=B1+B3+B5
B1 directed downwards according to right hand thumb rule
B3directed upwards according to right hand thumb rule
B5directed downwards according to right hand thumb rule
So,Bp=B1+B3B5
B due to a circular current carrying conductor at it's centre is given by:
B=μ0i4πr.θ
So,Bp=μ0i4πR.θ+μ0i4π2R.θμ0i4π3R.θ
|Bp|=|μ0i4πR.θ[112+13]|
|Bp|=μ0i4πR.56
|Bp|=(μ0i4π).5iθ6R
Hence the correct answer is C

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