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  • How to solve this problem- A current loop, having two circular arcs joined by two radial lines is shown in the figure. It carries a current of 10 A. The magnetic field at point O will be close to:

 

A current loop, having two circular arcs joined by two radial lines is shown in the figure. It carries a current of 10 A. The magnetic field at point O will be close to:

  • Option 1)

     1.0\times 10^{-7}T

       

      

      

  • Option 2)

    1.5\times 10^{-7}T

  • Option 3)

    1.5\times 10^{-5}T

  • Option 4)

    1.0\times 10^{-5}T

Answers (1)

best_answer

 

Arc subtends angle theta at the centre -

B=\frac{\mu_{0}}{4\pi }.\frac{\theta i}{r}

- wherein

Radius of arc

QR = 3 cm = r1

PS = 5 cm = r2

Magnetic field due to an arc  = \frac{M_{O}I}{4 \pi r} \theta

So,

Magnetic field at O

= B_{QR} - B_{PS} (Since current is in opposite direction )

= \frac{M_{O}I}{4 \pi } \theta \left [ \frac{1}{3} - \frac{1}{5} \right ] \times \frac{1}{10^{-2}}

= \frac{4 \pi \times 10 ^{-7} \times 10}{4 \pi} \times \frac{\pi}{4} \times \frac{2}{15} \times 10^{2}

=\frac{\pi}{3} \times 10^{-5}

= 1 x 10-5 T

 


Option 1)

 1.0\times 10^{-7}T

   

  

  

Option 2)

1.5\times 10^{-7}T

Option 3)

1.5\times 10^{-5}T

Option 4)

1.0\times 10^{-5}T
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