13. Electric Fields

Electric Fields Coulomb’s law of Electrostatic Force – The magnitude of the electrostatic force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of their separation. Electric Potential Energy – work done by an external agent on the charge in moving the charge from infinity to that point. E 2 0 qQF 4r 2 0 QE 4r 0 qQU 4r 0 QV 4r Note:  May not need n egative sign for charges in FE and E (Vectors)  Must sub in respective negative signs for charges in U and V. Electric Field Strength, E – at a point in an electric field is the electric force per unit positive charge acting on a stationary test charge placed at that point. Electric Potential, V – work done per unit positive charge by an external agent in moving a point charge from infinity to that point. Field Lines  Tangent of the lines points in the direction of the force on a positive test charge  Point in the direction of decreasing electric potentials  Closer lines indicate larger E  No two lines intersect one another  Perpendicular to Equipotential Lines/Surfaces Equipotential Lines  All points along a line has the same electric potential  No work done when moving a mass along a equipotential line  Perpendicular to Field Lines One point charge: Two like point charges r Q -Q FG FG Opposite charges attract Like charges repel r FG FG Q Q r -Q E Point P r Q E Point P E dUF dr GFE q dVE dr r V E dr   r EU F dr   FE = qE UV q U = qV

Two unlike point charges In between parallel plates, Electric is uniform, assuming d << L Electric Field Strength, VE d  Electric Force on a charge q, VF qE q d  Work Done / Change in EPE W q V Parallel Plates: *Usually assume field in between plates to be uniform. Non-uniform field at the edges are usually ignored in calculation. Electric Field Strength and Potential in Conductors:  E is zero but V maybe non-zero within a conductor. o Because net charges will distribute over the surface of (but not within) the conductor.  Charge density is larger at region of smaller radius of curvature  Since E = 0, and E = -dV/dr, there is no change in potential  equipotential throughout the conductor. (Note: same potential does not mean zero potential) d L

Projectile Motion of a Charge Moving in Between Parallel Plates Force on charge -q VFq d  , upward Acceleration on charge -q y F q Va m md  Equations of Motion  ux remains constant  Applicable only within plates, in the uniform field y-directions x-direction 2 y y y 1s u t a t 2 xxs u t 22 y y y yv u 2a s 22 xxvu  xxvu y y yv u a t Final Velocity xyv u v 22 xyv u v Time of Flight (Time within Plates) f x Lt u , t = 0 when charge just enter plates Angle of deflection, θ At time tf just after leaving the plates, y1 x vtan u  Will charge hit plate or leave the plates? At time tf just after leaving the plates, lys   hits plate lys   leaves plate lys   just nice leave plate Conservation of Energy  Electric Potential Energy converted to Kinetic Energy of the charge y 22 f i s y 11mv mv q V qEs22    d L θ -q ux Straight path outside the plates l