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PHY132_L07

# PHY132_L07 - Classical Physics II Classical Physics II...

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lassical Physics II Classical Physics II PHY132 Lecture 7 Capacitance Lecture 7 1 02/08/2010

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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: oulomb’s Law for point- ke charges: 1 Qq r ± enclosed 0 closed surface E Q d ε Φ= = EA v Coulomb s Law for point like charges: • Electric Potential: 2 0 4 E r πε Fr – potential energy change: Δ U E =– W ork done by E – electric potential: V = U E / q test . 2 V r 02/08/2010 Lecture 7 2 1 21 ( ) and: dV VV V d d Δ= = = r rr E s E r
Capacitance i h i t ib t i m th SOURCE f th l t i A given charge distributrion Q ( r ) forms the SOURCE of the electric field E ( r ) i.e. at ANY space point r = ( x , y , z ) , the force-per-unit-test-charge E = a vector with magnitude and direction F Q / q test is a vector with magnitude and direction): E = E [ Q ( r )] Given an electric field E ( r ) , (a CONSERVATIVE force field), every s pace point can be assigned a unique POTENTIAL ENERGY U ( r ) , or – equivalently – a POTENTIAL V ( r ) (the potential energy-per-unit- test charge): U ( r ) W ( r 0 r ) = – r 0 r d l = r r 0 d l or: V ( r ) U ( r )/ q test = – W/q test = r r 0 d l Thus: V ( r ) = r d l = V { E [ Q ( r )]} Lecture 7 4 Capacitance is defined as: C Q ( r )/ V ( r ) or: Q = CV 02/08/2010

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the Capacitance the Capacitance of a Sphere of a Sphere e.g. a point charge Q (or outside a spherically-symmetric charge distribution): 2 0 1 () 4 Q r r
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PHY132_L07 - Classical Physics II Classical Physics II...

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