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QJEEM19Ph44bc: JEE Main 2019 Physics - Class 12 JEEM19Ph44bc Solution: One of the two identical conducting wires of length L is bent…

One of the two identical conducting wires of length L is bent in the form of a circular loop and the other one into a circular coil of N identical turns. If the same current is passed in both, the radio of the magnetic field at the central of the loop (BL) to that at the center of the coil (BC), i.e. BLBC{{{B_L}} \over {{B_C}}} will be :

Multiple Choice Options

  • A N
  • B 1N{1 \over N}
  • C N2
  • D 1N2{1 \over {{N^2}}}

Step-by-Step Verified Solution

JEE Main 2019 (Online) 9th January Evening Slot Physics - Magnetic Effect of Current Question 165 English Explanation
For loop,

L = 2 π\pi R

For coil,

L = N ×\times 2 π\pi r

∴\therefore    2 π\pi R = N ×\times 2 π\pi r

⇒\Rightarrow   R = Nr

⇒\Rightarrow   r = RN{R \over N}

We know,

BL = μ0i2R{{{\mu _0}i} \over {2R}}

and  BC = N ×\times μ0i2r{{{\mu _0}i} \over {2r}}

∴\therefore    BLBC=μ0i2RN×μ0i2(RN)=1N2{{{B_L}} \over {{B_C}}} = {{{{{\mu _0}i} \over {2R}}} \over {N \times {{{\mu _0}i} \over {2\left( {{R \over N}} \right)}}}} = {1 \over {{N^2}}}

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