So you have that $\vec{B} = \frac{a}{r^2}\begin{bmatrix}0 & z & -y\end{bmatrix}$ thus the magnitude is $B = \frac{a}{r^2}\sqrt{z^2+(-y)^2},$ where $a$ is unknown.

Can you write that as a function of $r?$

Can you investigate what happens as $r$ goes to zero?

Are magnetic fields continuous in empty space (a vacuum)?

If so, try the next five:

What magnetic field do you expect at the origin?

What is its magnitude?

Remember that $a$ is an unknown constant. Is there any choice of $a$ that allows $B$ to approach the magnitude it needs as you approach the origin?

Is it the only choice? Is it what you wanted?

If not, can you compute the line integral of the magnetic field in a circle about the origin and compare that to some thing?

So you have that $\vec{B} = \frac{a}{r^2}\begin{bmatrix}0 & z & -y\end{bmatrix}$ thus the magnitude is $B = \frac{a}{r^2}\sqrt{z^2+(-y)^2},$ where $a$ is unknown.

Can you write that as a function of $r?$

Can you investigate what happens as $r$ goes to zero?

Are magnetic fields continuous in empty space (a vacuum)?

If so, try the next five:

What magnetic field do you expect at the origin?

What is its magnitude?

Remember that $a$ is an unknown constant. Is there any choice of $a$ that allows $B$ to approach the magnitude it needs as you approach the origin?

Is it the only choice? Is it what you wanted?

If not, can you compute the line integral of the magnetic field in a circle about the origin and compare that to some thing?

For educational purposes I can share some actual requirements of continuity. Across any surface bounded by a triangle the normal component of the $\vec B$ field must give the same average flux just on one side of the triangle as on the other (or else you can't take the divergence and hence you can't say the divergence is zero).

There is a similar rule for tangential components but they can jump depending one whether you have surface currents or if something super extreme is happening to an electric field in a particular instant.

So you have that $\vec{B} = \frac{a}{r^2}\begin{bmatrix}0 & z & -y\end{bmatrix}$ thus the magnitude is $B = \frac{a}{r^2}\sqrt{z^2+(-y)^2},$ where $a$ is unknown.

Can you write that as a function of $r?$

Can you investigate what happens as $r$ goes to zero?

What magnetic field do you expect at the origin?

What is its magnitude?

Remember that $a$ is an unknown constant. Is there any choice of $a$ that allows $B$ to approach the magnitude it needs as you approach the origin?

Is it the only choice? Is it what you wanted?

So you have that $\vec{B} = \frac{a}{r^2}\begin{bmatrix}0 & z & -y\end{bmatrix}$ thus the magnitude is $B = \frac{a}{r^2}\sqrt{z^2+(-y)^2},$ where $a$ is unknown.

Can you write that as a function of $r?$

Can you investigate what happens as $r$ goes to zero?

Are magnetic fields continuous in empty space (a vacuum)?

If so, try the next five:

What magnetic field do you expect at the origin?

What is its magnitude?

Remember that $a$ is an unknown constant. Is there any choice of $a$ that allows $B$ to approach the magnitude it needs as you approach the origin?

Is it the only choice? Is it what you wanted?

If not, can you compute the line integral of the magnetic field in a circle about the origin and compare that to some thing?