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- Homework Statement
- In a region of space there is a constant magnetic field ##\vec{B}=B(3,2,1)##, where ##B## is constant. What is the flux of the magnetic field through the lateral surface of a cylinder present in that region of space?

- Relevant Equations
- ##\phi_{S\text{ closed}}(\vec{B})=\int_{S\text{ closed}}\vec{B}\cdot d\vec{S}=0##

If the question had been asking about the flux through the whole surface of the cylinder I would have said that the flux is 0, but since it is asking only about the lateral surfaces I am wondering how one could calculate such a flux not knowing how the cylinder is oriented in space. One could for example take a cylinder whose axis lies on the line spanned by the vector ##(3,2,1)## and say that the flux through the lateral surface of the cylinder is 0. So, the answer in this case depends on the orientation of the cylinder in space, am I right?

Or is there a way to find out the flux even without knowing anything more specific about the cylinder?

Thanks.

Or is there a way to find out the flux even without knowing anything more specific about the cylinder?

Thanks.