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# Hwk2_additional_solutions - Homework 2 solutions 2.3 Find...

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2.3 Find the potential energy of a uniformly charged sphere of charge Q and radius R by integrating (a) , ρφ (b) E 2 . The charge density insider the sphere is 3 3 4 . Q R ρ π = Hence the electric field is 3 2 , , / , . Qr R r R E Q r r R < = The potential is then 2 3 3 , , 2 2 , . Q Qr r R R R Q r R r φ - < = (a) The potential energy is 2 2 5 2 2 3 3 3 4 2 all space 0 0 1 1 3 3 3 3 4 . 2 2 4 2 2 4 5 5 R R Q Q Qr Q r Q U dV r dr r R R R R R R = = - = - = (b) Also 2 2 2 5 2 2 2 2 2 3 2 6 all space 0 0 1 1 1 3 4 4 . 8 8 2 5 2 5 R R R R Qr Q Q r Q Q U E dV r dr r dr R r R r R = = + = + - = 2.4 Find the dipole moment of : (a) a straight wire of length L with a linear charge density ( ) 2 , 2, qz z z L L λ = < 2 cos . q R σ θ θ =

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Hwk2_additional_solutions - Homework 2 solutions 2.3 Find...

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