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  • The magnetic field due to a current carrying circular loop of radius 3 cm at a point on its axis at a distance of 4 cm from the centre is 54 T. The magnetic field (in<img alt="\mu \mathrm

The magnetic field due to a current carrying circular loop of radius 3 cm at a point on its axis at a distance of 4 cm from the centre is 54 T. The magnetic field (in\mu \mathrm{T}  ) at the centre of the loop will be
 

Option: 1

250


Option: 2

150


Option: 3

125


Option: 4

72


Answers (1)

best_answer

Given \mathrm{x=4 \mathrm{~cm}=0.04 \mathrm{~m}}  and\mathrm{ r=3 \mathrm{~cm}=0.03 \mathrm{~m}}. The magnetic field at a point on the axis of the loop is given by
\mathrm{ B=\frac{\mu_o I r^2}{2\left(r^2+x^2\right)^{3 / 2}} }
Magnetic field at the centre of the coil is given by
\mathrm{ B_0=\frac{\mu_o I}{2 r} }
on Dividing , we get
\mathrm{ \frac{B_0}{B}=\frac{r^3}{\left(r^2+x^2\right)^{3 / 2}} }
Substituting the values of r and x, we get

\mathrm{ \frac{B_0}{B}=\frac{125}{27} }

or

\mathrm{ \quad B_0=\frac{125}{27} B=\frac{125}{27} \times 54 \mu \mathrm{T}=250 \mu \mathrm{T} }

Hence the correct choice is (a).

Posted by

SANGALDEEP SINGH

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