PHY132_L08 - Classical Physics II Classical Physics II...

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lassical Physics II Classical Physics II PHY132 Lecture 8 Capacitance, Dielectrics, and Stored Energy Lecture 8 1 02/12/2010
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Recap • Electric Field E – Generated by charged “sources”, – VECTOR field that pervades all space: E =( E ( r ), E ( r ), E ( r )) x y z – a “test charge” interacts with E and experiences a force F =q E . – may be represented by “field lines”, giving direction and strength • Gauss’ Law: – Coulomb’s Law for point-like charges: 2 1 E Qq Fr enclosed 0 closed surface E Q d  EA • Electric Potential: – potential energy change: Δ U E =– W ork done by E 0 4 r  – electric potential: V = U E / q test . •Capacitance: 2 1 21 ( ) and: dV VV V d d  r r rr E s E r C Q ( r )/ V ( r ) or: Q = CV 02/12/2010 Lecture 8 2
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the Potential energy of the arrangement of ree charges below equals three charges below equals … A. 3 kq 2 / L 2 q . q B. 2 kq 2 / L C. 3 kq 2 / L L L D. not simply calculable without calculator … L q q 02/12/2010 Lecture 8 3
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a Spherical a Spherical Capacitor Capacitor A charged set of concentric (conducting) spheres of radii a and b>a , with charges + Q and Q respectively: 2 1 ( ) (for ; elsewhere 0!) Q ra r b E  Er 0 4 r  y Q test 11 1 bb Qd r Q Qq r q  test test () Vb a Wb V aq W a bq a b V  x b a Q E =0 E =0 test 2 2 0 00 4 44 aa dr q r rb a    0 QQ b a ab a b   E concentric spheres 0 of radii , 4 ab a Qa b C Vb a  Note: C depends only on geometrical quantities (i.e. sizes)! Lecture 8 4 02/12/2010
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