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  • Stuck here, help me understand: - One of the two identical conducting wires of length L is bent in the form of a circular loop and the - Magnetic Effects of Current and Magnetism - JEE Main

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 same current is passed in both, the ratio of the magnetic field at the central of the loop (BL) to that at the centre of the coil (BC), i.e. \frac{B_{L}}{B_{C}} will be:

 

 

  • Option 1) N

     

  • Option 2) 1/n2

     

  • Option 3) 1/n

     

  • Option 4) N2

     

     

Answers (1)

best_answer

 

Magnetic field due to circular Current Carrying arc -

B=\frac{\mu_{o}}{4\pi}\:\frac{2\pi i}{r}=\frac{\mu_{o}i}{2r}

- wherein

Circular loop : Let R be radius 

B_{L}=\frac{\mu _{o}i}{2R}

Circular Coil : Let r be radius 

B_{C}=\frac{\mu _{o}Ni}{2r}

L=N\times 2\pi r=2\pi R

=>r=\frac{R}{N}

\therefore  B_{C}=\frac{\mu _{o}N^{2}i}{2R}

\frac{B_{L}}{B_{C}}=\frac{1}{N^{2}}

 


Option 1)

N

Option 2)

\frac{1}{N^{2}}

Option 3)

 

\frac{1}{N}

Option 4)

 

N2

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