Electricity Potential - General Physcis - Lecture Slides, Slides of Physics

Download Electricity Potential - General Physcis - Lecture Slides and more Slides Physics in PDF only on Docsity! Short Version : 22. Electric Potential Docsity.com 22.1. Electric Potential Difference Conservative force: AB B AU U U   ABW  B A d   F r Electric potential difference  electric potential energy difference per unit charge B A d   E rABAB UV q    BV if reference potential VA = 0. [ V ] = J/C = Volt = V For a uniform field: AB ABV   E r  B A   E r r ( path independent ) rAB E Docsity.com Example 22.2. Charged Sheet An isolated, infinite charged sheet carries a uniform surface charge density . Find an expression for the potential difference from the sheet to a point a perpendicular distance x from the sheet.  0 0xV E x    02 x    E Docsity.com 22.2. Calculating Potential Difference Potential of a Point Charge AB B AV V V   B A d   E r 2 ˆ B A k q d r    r r 2 B A r AB r k qV d r r    ˆ ˆ ˆd d r  r r r r d r 1 1 B A k q r r          For A,B on the same radial For A,B not on the same radial, break the path into 2 parts, 1st along the radial & then along the arc. Since, V = 0 along the arc, the above equation holds. Docsity.com The Zero of Potential Only potential differences have physical significance. Simplified notation: RA A R AV V V V    R = point of zero potential VA = potential at A. Some choices of zero potential Power systems / Circuits Earth ( Ground ) Automobile electric systems Car’s body Isolated charges Infinity Docsity.com Finding Potential Differences Using Superposition Potential of a set of point charges:   i i P i qV P k  r r Potential of a set of charge sources:    i i V P V P  Docsity.com Example 22.5. Dipole Potential An electric dipole consists of point charges q a distance 2a apart. Find the potential at an arbitrary point P, and approximate for the casewhere the distance to P is large compared with the charge separation.     1 2 qqV P k k r r    1 2 1 1kq r r        2 2 2 1 2 cosr r a r a    2 2 2 2 2 cosr r a r a    2 2 2 1 4 cosr r r a     2 1 1 2r r r r   r >> a  2 1 2 cosr r a     2 12 r rV P k q r   2 2 cosqak r   2 cospk r   p = 2qa = dipole moment 2 1 2 1 r rkq r r   +q: hill q: hole V = 0 Docsity.com Continuous Charge Distributions Superposition: V dV  d qk r  dVk r        3d r V k      r r r r Docsity.com 22.3. Potential Difference & the Electric Field W = 0 along a path  E  V = 0 between any 2 points on a surface  E. Equipotential  Field lines. Equipotential = surface on which V = const. V > 0 V < 0 V = 0 Steep hill Close contour Strong E Docsity.com Calculating Field from Potential B A r AB r V d    E r  dV d  E r i i i E dx  i i i V d x x     i i VE x     V E =  ( Gradient of V ) V V V x y z             E i j k E is strong where V changes rapidly ( equipotentials dense ). Docsity.com Example 22.8. Charged Disk Use the result of Example 22.7 to find E on the axis of a charged disk. Example 22.7:    2 222k QV x x a xa   2 2 2 2 1k Q x a x a         x VE x     x > 0 x < 0 0y zE E  dangerous conclusion Docsity.com Consider 2 widely separated, charged conducting spheres. 1 1 1 QV k R  22 2 QV k R  Their potentials are If we connect them with a thin wire, there’ll be charge transfer until V1 = V2 , i.e., 1 2 1 2 Q Q R R    24 j j j Q R    In terms of the surface charge densities 1 1 2 2R R we have  Smaller sphere has higher field at surface.  1 1 2 2E R E R  Same V Docsity.com Ans. Surface is equipotential  | E | is larger where curvature of surface is large.  More field lines emerging from sharply curved regions. From afar, conductor is like a point charge. Conceptual Example 22.1. An Irregular Condutor Sketch some equipotentials & electric field lines for an isolated egg-shaped conductor. Docsity.com Conductor in the Presence of Another Charge Charged sphere is isolated and field is symmetric . . . ... but the presence of a nearby charge breaks the symmetry. E = E ee ® Docsity.com