[tex]\mathbf{F}(x,y,z)=(x^2+yz,y^2+zx,-2z(x+y))[/tex] Find the vector potential.(adsbygoogle = window.adsbygoogle || []).push({});

A vector potential [tex]\mathbf{V}[/tex] would have to satisfy

[tex]\mathbf{V}_x=x^2+yz[/tex]

[tex]\mathbf{V}_y=y^2+zx[/tex]

[tex]\mathbf{V}_z=-2z(x+y)[/tex]

So,

[tex]\mathbf{V}=\frac{x^3}{3}+xyz+M(y)+N(z)[/tex]

[tex]\Rightarrow \mathbf{V}_y=zx+M_y(y)[/tex]

[tex]\Rightarrow M_y(y)=y^2[/tex]

[tex]\Rightarrow \mathbf{V}=\frac{x^3}{3}+xyz+\frac{y^3}{3}+N(z)[/tex]

[tex]\Rightarrow \mathbf{V}_z=xy+N_z(z)[/tex]

However, here I can't find [tex]N_z(z)[/tex].

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# Homework Help: Finding the Vector Potential

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