Integration Path - General Physics - Solved Past Paper, Exams of Physics

Download Integration Path - General Physics - Solved Past Paper and more Exams Physics in PDF only on Docsity! 2. (30 pts) A conducting cylindrical shell of radius R carries current I out of the page as shown below. R a) (15 pts) Find the magnetic field ~B at a point inside the hollow in the cylindrical shell (r < R). Show your work. You may indicate the direction on the figure above. In this case, use the red dashed circle as the integration path for Ampere’s Law. There is no current enclosed by this loop, so we have ∮ ~B · d~ℓ = µ0I = 0 Thus the magnetic field is zero. b) (15 pts) Find the magnetic field ~B at a point outside the cylindrical shell (r > R). Show your work. You may indicate the direction on the figure above. Since we want the magnetic field outside of the shell, use the blue dashed circle as the integration path. Now there is current enclosed, in fact all of the current! So we have ∮ ~B · d~ℓ = µ0I 2πrB = µ0I B = µ0I 2πr Since there are no other numbers, we may as well leave it like this (though you could plug in µ0 and simplfy a little).