Need help finding the magnatic b feild

[leonne]

Homework Statement

got a question abotu the bfield ex a long wire carries current I ( the current flows down the surface of the inner cylinder, radius a back along the outer cylinder radius B

Homework Equations

The Attempt at a Solution

So i found the B field to be B=$$\mu$$I/(2$$\pi$$S) but they got the same thing but has a $$\widehat{}\phi$$ vector. My question is when do i know when i need a vector? Alot of the homework I did the B field was just what I had, but need to know to be able use the poyntin vector which has a cross product of E X B Also same thing with E field what do i need to look for?
thanks

 

[mark726]

Dear student,

Thank you for your question. The use of vectors in electromagnetic fields is determined by the geometry of the problem. In the case of a long wire carrying current, the magnetic field is in the form of concentric circles around the wire. In this case, we can use the right hand rule to determine the direction of the magnetic field vector. However, in more complex geometries, such as a loop of wire or a solenoid, the magnetic field may have components in multiple directions and we would need to use vectors to accurately describe it.

Similarly, the electric field also depends on the geometry of the problem. In most cases, the electric field is in the same direction as the electric force, which can be determined using the right hand rule for positive charges. However, in cases where the electric field is not in the same direction as the electric force, we would need to use vectors to accurately describe it.

In general, when solving problems in electromagnetism, it is important to carefully consider the geometry and use the appropriate vector notation to accurately describe the fields. I hope this helps to clarify your question. Best of luck with your studies!