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Homework Statement:
 We know that the magnetic field ##\vec B## can be expressed as a curl of the vector potential ##\vec A##. Invert this equation to express the vector potential in terms of the magnetic field.
Relevant Equations:

We have the magnetic field : ##\vec B = \vec \nabla \times \vec A##.
We can also show that if the linear velocity ##\vec v## of a point on a rigid body with position velocity ##\vec r## can be expressed in terms of the angular velocity ##\vec \omega## as ##\vec v = \vec \omega \times \vec r##, then ##\vec \omega = \frac{1}{2} \vec \nabla \times \vec v##.
My solution is making an analogy of the ##\text{Relevant equations}## as shown above, starting from the equation ##\vec \omega = \frac{1}{2} \vec \nabla \times \vec v##.
We have ##\vec B = \vec \nabla \times \vec A = \frac{1}{2} \vec \nabla \times 2\vec A \Rightarrow 2\vec A = \vec B \times \vec r##, whereupon I make the analogy with velocity (##\vec v \rightarrow 2\vec A) ##and angular velocity (##\vec \omega \rightarrow \vec B)## vectors as stated above.
Hence we have ##\mathbf{\boxed{\vec A = \frac{1}{2} \vec B \times \vec r}}## as the desired equation.
Is this correct?
We have ##\vec B = \vec \nabla \times \vec A = \frac{1}{2} \vec \nabla \times 2\vec A \Rightarrow 2\vec A = \vec B \times \vec r##, whereupon I make the analogy with velocity (##\vec v \rightarrow 2\vec A) ##and angular velocity (##\vec \omega \rightarrow \vec B)## vectors as stated above.
Hence we have ##\mathbf{\boxed{\vec A = \frac{1}{2} \vec B \times \vec r}}## as the desired equation.
Is this correct?
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