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Maxwellkid

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This is a simple problem if you work with only magnitude and consider the symmetry of a ring. However, I am taking a detailed approach, and I am not getting the correct answer. Could you please look over my math???

a evenly distributed ring of charge on the positive Y-Z plane has a current, I, flowing counterclockwise or flowing from positive Z direction on top and -Z direction on bottom of ring. Figure out the magnetic field along the X axis of this ring of charge from the center of the ring.

[tex] d \vec{B} = \frac {\mu_{o} I}{4\pi} \frac {d\vec{l} \times \hat{r}}{r^2}[/tex]

below are pictures of the ring of charge. left picture is the sideway view with theta being constant. right picture is the frontal view with phi.

[tex] d\vec{l} = <0 , dl cos\phi , dl sin\phi>[/tex]

[tex] \hat{r} = <cos\theta , -w/r sin\phi , w/r cos\phi> [/tex]

[tex]{d\vec{l} \times \hat{r} = \frac{w}{r} cos^2\phi dl \cdot \hat{i} + \frac{w}{r} sin^2\phi dl \cdot \hat{i} + cos\theta sin\phi dl \cdot \hat{j} - cos\theta cos\phi dl \cdot \hat{k} [/tex]

[tex]\frac {d\vec{l} \times \hat{r}}{r^2} =\frac{w}{r^3} 1 dl \cdot \hat{i} +\frac{1}{r^2} cos\theta sin\phi dl \cdot \hat{j} - \frac{1}{r^2} cos\theta cos\phi dl \cdot \hat{k}[/tex]

[tex] dl = w d\phi [/tex]

[tex]\frac {d\vec{l} \times \hat{r}}{r^2} = \frac{w^2}{r^3} 1 d\phi \cdot \hat{i} +\frac{w}{r^2} cos\theta sin\phi d\phi \cdot \hat{j} - \frac{w}{r^2} cos\theta cos\phi d\phi \cdot \hat{k}[/tex]

ARE ALL MY STEPS CORRECT SO FAR????

a evenly distributed ring of charge on the positive Y-Z plane has a current, I, flowing counterclockwise or flowing from positive Z direction on top and -Z direction on bottom of ring. Figure out the magnetic field along the X axis of this ring of charge from the center of the ring.

[tex] d \vec{B} = \frac {\mu_{o} I}{4\pi} \frac {d\vec{l} \times \hat{r}}{r^2}[/tex]

below are pictures of the ring of charge. left picture is the sideway view with theta being constant. right picture is the frontal view with phi.

[tex] d\vec{l} = <0 , dl cos\phi , dl sin\phi>[/tex]

[tex] \hat{r} = <cos\theta , -w/r sin\phi , w/r cos\phi> [/tex]

[tex]{d\vec{l} \times \hat{r} = \frac{w}{r} cos^2\phi dl \cdot \hat{i} + \frac{w}{r} sin^2\phi dl \cdot \hat{i} + cos\theta sin\phi dl \cdot \hat{j} - cos\theta cos\phi dl \cdot \hat{k} [/tex]

[tex]\frac {d\vec{l} \times \hat{r}}{r^2} =\frac{w}{r^3} 1 dl \cdot \hat{i} +\frac{1}{r^2} cos\theta sin\phi dl \cdot \hat{j} - \frac{1}{r^2} cos\theta cos\phi dl \cdot \hat{k}[/tex]

[tex] dl = w d\phi [/tex]

[tex]\frac {d\vec{l} \times \hat{r}}{r^2} = \frac{w^2}{r^3} 1 d\phi \cdot \hat{i} +\frac{w}{r^2} cos\theta sin\phi d\phi \cdot \hat{j} - \frac{w}{r^2} cos\theta cos\phi d\phi \cdot \hat{k}[/tex]

ARE ALL MY STEPS CORRECT SO FAR????

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