Unformatted text preview: you can assume that the magnetic ﬁeld generated by these moving charges is negligible.) 3) (J5.3) A right circular solenoid of ﬁnite length L and radius a has N turns per unit length and carries a current I . Show that the magnetic induction on the cylinder axis in the limit NL → ∞ is B z = μ NI 2 (cos θ 1 + cos θ 2 ) where the angles are deﬁned in the ﬁgure. 2 θ θ 1 4) (J5.13) A sphere of radius a carries a uniform surfacecharge distribution σ . The sphere is rotated about a diameter with constant angular speed ω . Find the vector potential and magneticﬂux density both inside and outside the sphere. Hint: Decompose the Y ‘m ’s into e.g., (ˆ y cos φˆ x sin φ )sin θ ∼i 2 [ˆ x ( Y 1 , 1 + Y 1 ,1 ) + i ˆ y ( Y 1 , 1 + Y 1 ,1 )]...
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 '11
 MARLOW
 Physics, Magnetism, Laplace, Magnetic Field, Princeton University, solid conducting sphere

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