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  • As shown in the figure, a long straight conductor with semicircular arc of radius <img alt="\frac{\pi }{10}m" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cfrac%7B%5Cpi%20%7D%7B10%7D

As shown in the figure, a long straight conductor with semicircular arc of radius \frac{\pi }{10}m is carrying current I = 3 A. The magnitude of the magnetic field. at the center O of the arc is : (The permeability of the vacuum 4 \pi \times 10^{-7} \mathrm{NA}^{-2})

Option: 1

1 \mu T


Option: 2

3 \mu \mathrm{T}


Option: 3

4 \mu T


Option: 4

6 \mu \mathrm{T}


Answers (1)

best_answer

\text { Given: } \mathrm{R}=\frac{\pi}{10} \mathrm{~m}, \quad \mathrm{I}=3 \mathrm{~A}, \quad \mu_0=4 \pi \times 10^{-7} \mathrm{~N} / \mathrm{A}^2

Magnetic field due to semi-circular arc is

\begin{aligned} & \mathrm{B}=\frac{\mu_0 I}{4 R} \\ & B=\frac{\mu_0 \times 3}{4 \times\left(\frac{\pi}{10}\right)}=\frac{4 \pi \times 10^{-7} \times 3}{4 \times \frac{\pi}{10}} \\ & \mathrm{~B}=3 \mu \mathrm{T} \end{aligned}

Posted by

vishal kumar

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