91Ó°ÊÓ

1. Current is$56.2\mathrm{mA}$
2. Radius$a=5.72\mathrm{cm}$
3. Radius is$b=9.36\mathrm{cm}$

Semicircle wire generates a magnetic field that is half that of circle wire. We use the formula for magnetic field for semicircle, and the direction is given by right hand rule.

Formula:

$\mathbf{\%}\mathbf{}\mathit{M}\mathit{a}\mathit{t}\mathit{h}\mathit{T}\mathit{y}\mathit{p}\mathit{e}\mathbf{!}\mathit{T}\mathit{r}\mathit{a}\mathit{n}\mathit{s}\mathit{l}\mathit{a}\mathit{t}\mathit{o}\mathit{r}\mathbf{!}\mathbf{2}\mathbf{!}\mathbf{1}\mathbf{!}\mathit{A}\mathit{M}\mathit{S}\mathbf{}\mathit{L}\mathit{a}\mathit{T}\mathit{e}\mathit{X}\mathbf{.}\mathit{t}\mathit{d}\mathit{l}\mathbf{!}\mathit{A}\mathit{M}\mathit{S}\mathit{L}\mathit{a}\mathit{T}\mathit{e}\mathit{X}\mathbf{!}\mathbf{}\mathbf{\%}\mathbf{}\mathit{M}\mathit{a}\mathit{t}\mathit{h}\mathit{T}\mathit{y}\mathit{p}\mathit{e}\mathbf{!}\mathit{M}\mathit{T}\mathit{E}\mathit{F}\mathbf{!}\mathbf{2}\mathbf{!}\mathbf{1}\mathbf{!}\mathbf{+}\mathbf{-}\mathbf{}\mathbf{\%}\mathbf{}\mathit{f}\mathit{e}\mathit{a}\mathit{a}\mathit{g}\mathit{K}\mathit{a}\mathit{r}\mathit{t}\mathbf{1}\mathit{e}\mathit{v}\mathbf{2}\mathit{a}\mathit{q}\mathit{a}\mathit{t}\mathit{C}\mathit{v}\mathit{A}\mathit{U}\mathit{f}\mathit{e}\mathit{B}\mathit{S}\mathit{j}\mathit{u}\mathit{y}\mathit{Z}\mathit{L}\mathbf{2}\mathit{y}\mathit{d}\mathbf{9}\mathit{g}\mathit{z}\mathit{L}\mathit{b}\mathit{v}\mathit{y}\mathit{N}\mathit{v}\mathbf{2}\mathit{C}\mathit{a}\mathit{e}\mathit{r}\mathit{b}\mathit{b}\mathit{j}\mathit{x}\mathit{A}\mathit{H}\mathit{X}\mathbf{}\mathbf{\%}\mathbf{}\mathit{g}\mathit{a}\mathit{r}\mathit{m}\mathit{W}\mathit{u}\mathbf{51}\mathit{M}\mathit{y}\mathit{V}\mathit{X}\mathit{g}\mathit{a}\mathit{r}\mathit{u}\mathit{a}\mathit{v}\mathit{P}\mathbf{1}\mathit{w}\mathit{z}\mathit{Z}\mathit{b}\mathit{I}\mathit{t}\mathit{L}\mathit{D}\mathit{h}\mathit{i}\mathit{s}\mathbf{9}\mathit{w}\mathit{B}\mathit{H}\mathbf{5}\mathit{g}\mathit{a}\mathit{r}\mathit{u}\mathit{W}\mathit{q}\mathit{V}\mathit{v}\mathit{N}\mathit{C}\mathit{P}\mathit{v}\mathit{M}\mathit{C}\mathit{G}\mathbf{4}\mathit{u}\mathit{z}\mathbf{}\mathbf{\%}\mathbf{}\mathbf{3}\mathit{b}\mathit{q}\mathit{e}\mathit{e}\mathbf{0}\mathit{e}\mathit{v}\mathit{G}\mathit{u}\mathit{e}\mathit{E}\mathbf{0}\mathit{j}\mathit{x}\mathit{y}\mathit{a}\mathit{i}\mathit{b}\mathit{a}\mathit{i}\mathit{e}\mathit{Y}\mathit{l}\mathit{f}\mathbf{9}\mathit{i}\mathit{r}\mathit{V}\mathit{e}\mathit{e}\mathit{u}\mathbf{0}\mathit{d}\mathit{X}\mathit{d}\mathit{h}\mathbf{9}\mathit{v}\mathit{q}\mathit{q}\mathit{j}\mathbf{-}\mathit{h}\mathit{E}\mathit{e}\mathit{e}\mathit{u}\mathbf{0}\mathit{x}\mathit{X}\mathit{d}\mathit{b}\mathit{b}\mathbf{}\mathbf{\%}\mathbf{}\mathit{a}\mathbf{9}\mathit{f}\mathit{r}\mathit{F}\mathit{j}\mathbf{0}\mathbf{-}\mathit{O}\mathit{q}\mathit{F}\mathit{f}\mathit{e}\mathit{a}\mathbf{0}\mathit{d}\mathit{X}\mathit{d}\mathit{d}\mathbf{9}\mathit{v}\mathit{q}\mathit{a}\mathit{q}\mathbf{-}\mathit{J}\mathit{f}\mathit{r}\mathit{V}\mathit{k}\mathit{F}\mathit{H}\mathit{e}\mathbf{9}\mathit{p}\mathit{g}\mathit{e}\mathit{a}\mathbf{0}\mathit{d}\mathit{X}\mathit{d}\mathit{a}\mathit{r}\mathbf{-}\mathit{J}\mathit{b}\mathbf{9}\mathit{h}\mathit{s}\mathbf{0}\mathit{d}\mathit{X}\mathit{d}\mathbf{}\mathbf{\%}\mathbf{}\mathit{b}\mathit{P}\mathit{Y}\mathit{x}\mathit{e}\mathbf{9}\mathit{v}\mathit{r}\mathbf{0}\mathbf{-}\mathit{v}\mathit{r}\mathbf{0}\mathbf{-}\mathit{v}\mathit{q}\mathit{p}\mathit{W}\mathit{q}\mathit{a}\mathit{a}\mathit{e}\mathit{a}\mathit{a}\mathit{b}\mathit{i}\mathit{G}\mathit{a}\mathit{a}\mathit{i}\mathit{a}\mathit{a}\mathit{c}\mathit{a}\mathit{W}\mathit{a}\mathit{b}\mathit{e}\mathit{a}\mathit{a}\mathit{e}\mathit{a}\mathit{W}\mathit{a}\mathit{a}\mathit{u}\mathit{a}\mathit{a}\mathit{a}\mathit{O}\mathit{q}\mathit{a}\mathit{a}\mathit{a}\mathbf{}\mathbf{\%}\mathbf{}\mathit{b}\mathit{a}\mathit{a}\mathit{a}\mathit{a}\mathit{a}\mathit{a}\mathit{a}\mathit{a}\mathit{a}\mathit{p}\mathit{e}\mathit{G}\mathit{a}\mathit{a}\mathit{m}\mathit{O}\mathit{q}\mathit{a}\mathit{i}\mathit{a}\mathit{b}\mathit{g}\mathbf{2}\mathit{d}\mathit{a}\mathbf{9}\mathit{m}\mathit{a}\mathit{a}\mathit{l}\mathit{a}\mathit{a}\mathit{a}\mathit{p}\mathit{a}\mathit{q}\mathit{a}\mathit{a}\mathbf{8}\mathit{q}\mathit{a}\mathit{c}\mathit{q}\mathit{a}\mathit{H}\mathbf{8}\mathit{o}\mathit{q}\mathit{B}\mathit{c}\mathit{a}\mathit{W}\mathit{G}\mathbf{}\mathbf{\%}\mathbf{}\mathit{j}\mathit{b}\mathit{G}\mathit{a}\mathit{e}\mathit{q}\mathit{i}\mathit{U}\mathit{d}\mathit{e}\mathit{h}\mathit{a}\mathit{p}\mathit{a}\mathit{q}\mathit{a}\mathit{a}\mathbf{8}\mathit{q}\mathit{a}\mathit{c}\mathit{a}\mathit{a}\mathit{I}\mathbf{0}\mathit{a}\mathit{G}\mathit{a}\mathit{e}\mathit{q}\mathit{i}\mathit{W}\mathit{d}\mathit{a}\mathit{N}\mathit{a}\mathit{a}\mathit{m}\mathit{O}\mathit{u}\mathit{a}\mathit{a}\mathit{a}\mathit{a}\mathit{a}\mathit{a}\mathit{a}\mathbf{!}\mathbf{41}\mathit{C}\mathbf{1}\mathbf{!}\mathbf{}\mathbf{\$}\mathit{B}\mathbf{}\mathbf{=}\mathbf{}\mathbf{\backslash }\mathit{f}\mathit{r}\mathit{a}\mathit{c}\mathbf{\left\{}\mathbf{\right\{}\mathbf{\backslash }\mathit{m}\mathit{u}\mathbf{}\mathit{I}\mathbf{\backslash }\mathit{t}\mathit{h}\mathit{e}\mathit{t}\mathit{a}\mathbf{}\mathbf{\left\}}\mathbf{\right\}}\mathbf{\left\{}\mathbf{\right\{}\mathbf{4}\mathbf{\backslash }\mathit{p}\mathit{i}\mathbf{}\mathit{R}\mathbf{\left\}}\mathbf{\right\}}\mathbf{\$}\mathbf{\%}\mathbf{}\mathit{M}\mathit{a}\mathit{t}\mathit{h}\mathit{T}\mathit{y}\mathit{p}\mathit{e}\mathbf{!}\mathit{E}\mathit{n}\mathit{d}\mathbf{!}\mathbf{2}\mathbf{!}\mathbf{1}\mathbf{!}$uncaught exception: Invalid chunk

in file: /var/www/html/integration/lib/com/wiris/plugin/impl/HttpImpl.class.php line 68
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Now magnetic field for semicircle is as follows

$$\begin{gathered} B_1=\frac{{\mathrm{μ}}_{o}I\mathrm{θ}}{4\mathrm{Ï€²¹}} \\ =\frac{{\mathrm{μ}}_{o}I\mathrm{Ï€}}{4\mathrm{Ï€²¹}} \\ =\frac{{\mathrm{μ}}_{o}I}{4a} \end{gathered}$$

And for radius b it is as follows

$B_2=\frac{{\mathrm{μ}}_{o}I}{4b}$

So total magnetic field is as follows

role="math" localid="1662799565933" $$\begin{gathered} B=B_1+B_2 \\ =\frac{{\mathrm{μ}}_{\mathrm{o}}\mathrm{I}}{4\mathrm{a}}+\frac{{\mathrm{μ}}_{\mathrm{o}}\mathrm{I}}{4\mathrm{b}} \\ =\frac{{\mathrm{μ}}_{\mathrm{o}}\mathrm{I}}{4}(\frac{1}{\mathrm{a}}+\frac{1}{\mathrm{b}}) \\ =(4\mathrm{π}×{10}^{-7}{\mathrm{NA}}^{-2})×(56.2×{10}^{-3}\mathrm{A})(\frac{1}{0.0572\mathrm{m}}+\frac{1}{0.0936\mathrm{m}}) \\ =4.97×{10}^{-7}\mathrm{T} \end{gathered}$$

The direction of the magnetic field is given by the right-hand rule, and it is into the page.

Now dipole moment is given as follows

$\mathrm{μ}=IA$

Here

role="math" localid="1662799996915" $$\begin{gathered} A=\frac{\mathrm{Ï€}\left({\mathrm{a}}^2+{\mathrm{b}}^2\right)}{2} \\ =\frac{\mathrm{Ï€}\left({\left(0.0572\mathrm{m}\right)}^2+{\left(0.0936\mathrm{m}\right)}^2\right)}{2} \\ =0.0189{\mathrm{m}}^2 \end{gathered}$$

Now

$$\begin{gathered} \mathrm{μ}=\left(56.2×{10}^{-3}\mathrm{A}\right)\left(0.0189{\mathrm{m}}^2\right) \\ =1.06×{10}^{-3}{\mathrm{Am}}^2 \end{gathered}$$

Since the direction is the same as the magnetic field, so it is into the page.