LCTRIC & MAGNTIC FILDS I (STATIC FILDS) LC 05A D. Hanna A. Kils Assciate Pfess lectnics & Cmmnicatins ngineeing Depatment Faclty f ngineeing Cai Univesity Fall 0 f Static lecticity
lectic & Magnetic Fields I f Static lecticity Clmb s Law: Clmb q F F n q Q q mete Q F n q Q q 4 Pemittivity f fee space (F/m) / m 0 9 F / 36 m D. H. Kils, Fall 0
lectic & Magnetic Fields I f Static lecticity lectstatic Field Intensity ect: at p F q Q 4 / m p Q Field f a pint chage D. H. Kils, Fall 0
lectic & Magnetic Fields I f Static lecticity Spepsitin f lectstatic Field: i Q p at p N i q i 4 i i / m q i F Q nq at p q q i q N D. H. Kils, Fall 0
D. H. Kils, Fall 0 f Static lecticity lectic & Magnetic Fields I lectstatic Field f a cntinm f chages: x y z p at d dq 3 4 4
lectic & Magnetic Fields I f Static lecticity lectstatic Field Lines: The diectin f a field Line mst be in the diectin f the ttal field at the pint. The lines depat fm psitive chages and teminate n negative chages. The sface density f the lines cssing nmally an element f sface aea at a pint in space gives the magnitde f the field at this pint. The lines ae pen and nn-intesecting. D. H. Kils, Fall 0
lectic & Magnetic Fields I f Static lecticity lectstatic Field Lines f pint chages: Field Line f a psitive pint chage Field Line f a negative pint chage D. H. Kils, Fall 0
lectic & Magnetic Fields I f Static lecticity lectstatic Field Lines f a diple: D. H. Kils, Fall 0
lectic & Magnetic Fields I lectstatic Flx : f Static lecticity (.m) Definitin: The nmbe f field lines cssing nmally an aea f space in the field f electstatic system f chages d d ds ds ds ds cs ds S D. H. Kils, Fall 0 ds
lectic & Magnetic Fields I f Static lecticity lectstatic Flx Leaving a Pint Chage q : ds, S c ds q sin 0 0 d d 4 q 4 q q Clsed Sface S c D. H. Kils, Fall 0
lectic & Magnetic Fields I f Static lecticity Gass s Law f lectstatic Field: Statement: The ttal twad flx f the -field ve any clsed sface in fee space is eqal t the ttal chage enclsed by the sface divided by ds S c ds Q enclsed by S c Clsed Sface S c D. H. Kils, Fall 0
lectic & Magnetic Fields I f Static lecticity Gass s Law f lectstatic Field: q ds ds q ds 0 c S c q Clsed Sface S c D. H. Kils, Fall 0
lectic & Magnetic Fields I f Static lecticity Gass s Law f Distibted Chage: lmetic Chage distibtin: S c ds Sface Chage distibtin: S c ds S Linea Chage distibtin: S c ds L v s dv ds d D. H. Kils, Fall 0
lectic & Magnetic Fields I f Static lecticity Applicatins f Gass s Law: Field f a nifmly chaged spheical shell: Field inside the shell S c ds 4 0 a S s ds 0 Q a Gassian Sface Field tside the shell 4 Q 4 a Q Q 4 a D. H. Kils, Fall 0 a
lectic & Magnetic Fields I f Static lecticity Applicatins f Gass s Law: Field f a nifmly chaged slid sphee: Field inside the shell a a 3 C / m Field tside the shell a a 3 D. H. Kils, Fall 0 a
lectic & Magnetic Fields I f Static lecticity Applicatins f Gass s Law: Field f a nifmly chaged infinite cylindical shell: Field inside the shell S c ds a dz 0 0 L 0 L d 0 L C / a m dz Field tside the shell dz L a L dz D. H. Kils, Fall 0 a dz
lectic & Magnetic Fields I f Static lecticity Applicatins f Gass s Law: Field f a nifmly chaged infinite cylindical shell: L C / m L a L 0 a D. H. Kils, Fall 0
lectic & Magnetic Fields I f Static lecticity Applicatins f Gass s Law: Field f a nifmly chaged slid cylinde: Field inside the shell a a 3 C / m Field tside the shell a a D. H. Kils, Fall 0 a
lectic & Magnetic Fields I f Static lecticity Applicatins f Gass s Law: Field f a nifmly chaged infinite plane sface: S c ds Field abve the plane: Field belw the plane: S s ds s ds ds 0 ds s s z s z s C / m s s C / m z s ds z z D. H. Kils, Fall 0
lectic & Magnetic Fields I f Static lecticity Applicatins f Gass s Law: Field f a tw ppsitely chaged infinite plane sfaces: Field between the tw planes: s Field abve and belw the planes: z D. H. Kils, Fall 0 - - - - - - - - - - - s s s 0 + + + + + + + + + s s s s s z
lectic & Magnetic Fields I f Static lecticity Applicatins f Gass s Law: Cnclsin Gass s Law is a vey pwefl tl t calclate the electstatic field nly f symmetic chage distibtins. F nn-symmetic distibtins the integal in the LHS is vey difficlt t calclate, de t the difficlty t find a clsed sface f which the field is nmal t all its elements f sface aea D. H. Kils, Fall 0
lectic & Magnetic Fields I f Static lecticity Scala lectstatic Ptential ( ) : lementay wk dne by the electstatic fce when a chage Q mves fm P t P dw Fce F d Q d If the chage Q is mved by an extenal agent, hence the wk dne by the agent is: P Q d F P dw agent Q d dw agent Q d A scala qantity which depends nly n the field and the teminal pints D. H. Kils, Fall 0
lectic & Magnetic Fields I f Static lecticity Scala lectstatic Ptential ( ) : Definitin: The electstatic ptential diffeence is the wk dne by an extenal agent t mve a test chage Q fm P t P against the electstatic fce pe nit chage f Q P Q d F P P P dw agent Q P P d J lt / C Discss: The ptential diffeence is independent n the path between the tw pints. D. H. Kils, Fall 0
lectic & Magnetic Fields I f Static lecticity Scala lectstatic Ptential ( ) : The ptential diffeence is independent n the path between the tw pints. dw agent P P dw agent P P D. H. Kils, Fall 0
lectic & Magnetic Fields I f Static lecticity lectstatic Ptential at a pint in a finite system f chages d The LHS f the eqatin abve eads: The ptential f P in efeence t that f P P P P Q d F P In a system f finite chage distibtins we may assme that the ptential at infinity is ze and can be sed as a efeence t all ptentials in the system. p P d D. H. Kils, Fall 0
lectic & Magnetic Fields I f Static lecticity lectstatic Ptential f a pint in the field f a pint chage p P d P p P Q 4 d d sin d Q p Q 4 lt D. H. Kils, Fall 0
lectic & Magnetic Fields I f Static lecticity Spepsitin f lectstatic Ptential: i p i p N i qi 4 i lt q q q i q N D. H. Kils, Fall 0
x y z z y x,, z y x,, D. H. Kils, Fall 0 f Static lecticity lectic & Magnetic Fields I lectstatic Ptential f a cntinm f chages: p d dq 4 4 p z z y y x x dz dy dx / 4
lectic & Magnetic Fields I f Static lecticity lectstatic Ptential at a pint in an infinite system f chages HAS NO MANING Y can nly calclate the ptential diffeence between tw pints; since y may NOT assme that the ptential t be ze at infinity D. H. Kils, Fall 0
lectic & Magnetic Fields I f Static lecticity lectstatic Ptential diffeence between tw pints in an infinite line chage ds d S c L L P P L L L L d L ln L D. H. Kils, Fall 0 d P P
lectic & Magnetic Fields I Calclatin f f Static lecticity fm a given Ptential Fnctin ( x, y, z) The ptential fnctin is given while the magnitde and diectin f ae nknwns d d d d d cs d d cs Rate f change f ptential fnctin alng the diectin f d Maximm +ve if cs 80 D. H. Kils, Fall 0
lectic & Magnetic Fields I Calclatin f When 80 f Static lecticity d d fm a given Ptential Fnctin ( x, y, z) max The diectin f maximm incease f the ptential fnctin d d The magnitde f is eqal t the maximm ate f incease f the ptential fnctin The diectin f is ppsite t the diectin f the maximm ate f incease f the ptential fnctin D. H. Kils, Fall 0
lectic & Magnetic Fields I f Static lecticity The Gadient f a Scala Fnctin f ( x, y, z) A vect peat, peates pn a scala fnctin and defined by: f The diectin f is in the diectin f the maximm ate f incease f the fnctin f ( x, y, z) f The magnitde f is eqal t the maximm ate f incease f the fnctin f ( x, y, z) f f diectinf df d max f df d max D. H. Kils, Fall 0
lectic & Magnetic Fields I f Static lecticity Calclatin f fm a given Ptential Fnctin ( x, y, z) The magnitde f is eqal t the maximm ate f incease f the ptential fnctin The diectin f is ppsite t the diectin f the maximm ate f incease f the ptential fnctin D. H. Kils, Fall 0
D. H. Kils, Fall 0 f Static lecticity lectic & Magnetic Fields I xpansin f The Gadient f a Scala Fnctin ) Catesian Cdinates: z y x z f y f x f f ) Cylindical Cdinates: z z f f f f 3) Spheical Cdinates: f f f f sin
lectic & Magnetic Fields I xample: f Static lecticity D. H. Kils, Fall 0 Find the ptential fnctin and the electstatic field intensity n the axis f a hllw cicla disk f inne and te adii a and b espectively that caies a nifm chage density s C/m p s s z b a z z a b z z z x b a z z p( 0,0, z) R d d y
lectic & Magnetic Fields I f Static lecticity qiptential Sfaces: Sfaces ve which the ptential is cnstant f all pints n the sface 50 30 ( ) Q 4 70 Field and eqiptential sfaces f a pint chage D. H. Kils, Fall 0
lectic & Magnetic Fields I f Static lecticity qiptential Sfaces: 50 30 30 0 30 50 50 70 70 70 D. H. Kils, Fall 0
lectic & Magnetic Fields I f Static lecticity qiptential Sfaces: D. H. Kils, Fall 0
lectic & Magnetic Fields I f Static lecticity qiptential Sfaces: qiptential sface d ( x, y, z) d d S S d 0 cs 0 d S 0 0 0 lectic field lines mst be pependicla t the eqiptential sfaces in a system f static chages D. H. Kils, Fall 0
lectic & Magnetic Fields I f Static lecticity qiptential Sfaces: qiptential sface Since, the diectin f is ppsite t the diectin f the maximm ate f incease f the ptential fnctin d S lectic field lines mst be diected fm the sface f highe ptential twads the sface f lwe ptential D. H. Kils, Fall 0
lectic & Magnetic Fields I f Static lecticity 30 50 70 D. H. Kils, Fall 0
lectic & Magnetic Fields I f Static lecticity Cicital Law f Static lectic Field: P P d P P d d 0 Static electic field lines ae pen lines D. H. Kils, Fall 0
lectic & Magnetic Fields I f Static lecticity Ppeties f lectstatic Field Lines: The lines ae pen and nn-intesecting. The diectin f a field Line mst be in the diectin f the ttal field at the pint. The lines depat fm psitive chages and teminate n negative chages. The sface density f the lines cssing nmally an element f sface aea at a pint in space gives the magnitde f the field at this pint. The lines mst be pependicla t the eqiptential sfaces diected fm the sface f highe ptential t that f lwe ptential. D. H. Kils, Fall 0