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  • The magnate field due to a Current Carrying circular loop of radius at a point on its axis a

The magnate field due to a Current Carrying circular loop of radius 3cm at a point on its axis at a distance of 4cm4cm from the centre is 54 \, \mu \mathrm{T}. The magnetic field (in MT) at the centre of the loop will be

Option: 1

72


Option: 2

125


Option: 3

150


Option: 4

250


Answers (1)

best_answer

Given  \begin{aligned} & x=4 cm=0.04 \mathrm{~m} \\ \end{aligned}

             \begin{aligned} & r=3 cm=0.03 \mathrm{~m} \end{aligned}

B=\frac{\mu_0 I r^2}{2\left(r^2+x^2\right)^{3 / 2}} \& B_0=\frac{\mu_0 I}{2r}

So, \begin{aligned} \frac{B_0}{B}=\frac{r^3}{\left(r^2+x^2\right)^{3 / 2}} & =\frac{(0.03)^3}{\left((0.03)^2+(0.04)^2\right)^{3 / 2}} \\ \end{aligned}

                                           \begin{aligned} & =\frac{125}{27} \\ \end{aligned}

So, \begin{aligned} B_0 & =\frac{125}{27} \times B=\frac{125}{27} \times 54 \mu \mathrm{T}=250 \mu \mathrm{T} \end{aligned}

 

 

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Rishi

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