Electrostatics - Lecture Notes PDF

Electrostatics Dr. Emad Sayed 1  Origin of charge Coulomb's law Electric field Superposition of electric field 2 Dr. Emad Sayed  Origin of charge Charges occur only in discrete amounts = “quantized”. (Robert Millikan)...

Electrostatics Dr. Emad Sayed 1  Origin of charge Coulomb's law Electric field Superposition of electric field 2 Dr. Emad Sayed  Origin of charge Charges occur only in discrete amounts = “quantized”. (Robert Millikan) Q=Ne N: integer number e: electron charge (-1.6x10 -19C) or proton charge (1.6x10 -19C) The electric charge in an isolated system is conserved, but charges may be re-arranged, distributed or transferred. 3 Dr. Emad Sayed  Dynamic e.g. Electric Current Charges Static e.g. Photocopiers 4 Dr. Emad Sayed  Static charges Electrostatics Static charges are usually accumulate in insulators, either in the core or on their surfaces. Meanwhile, they populate only the surface of a conductor, where they are free to move inside the conductor. Grounding of machines and electric devices is necessary to avoid static charges. Static charges disappears with increasing of humidity Danger of electrostatics https://www.youtube.com/watch?v=XKAhx4NdJTs 5 Dr. Emad Sayed  Electric field of a static point charge The space around charge in which electric effects appear Coulomb’s law: The electric field (E) due to a point charge (q) at a point located a distance (r) from the charge is: q r Where “k” is called “Coulomb’s constant” = 9x109 N.m2/C2 6 Dr. Emad Sayed  “Coulomb’s constant” depends on the medium containing the charge Where is the “permittivity of air” = 8.85x10-12 C2/N.m2 Permittivity: The ability of the medium to sustain the field lines inside it. 7 Dr. Emad Sayed  Electric field lines Imaginary lines flowing in the space around the charge, and they are characterized by: 1- Lines are tangent to the direction of the field at any point. 2- The number of lines per unit area is proportional to the field strength. 3- Field lines start from a positive charge and end at a negative charge. 4- Lines are always perpendicular to the charge surface. 8 Dr. Emad Sayed 9 Dr. Emad Sayed  How to determine the field direction The sign of the charge affects the field direction: 10 Dr. Emad Sayed  Superposition of electric fields The resultant electric field at a given point due to a number of charges is the vector sum of electric field of the individual charges at this point: 11 Dr. Emad Sayed  This means: magnitude direction 12 Dr. Emad Sayed  Example What are the magnitude and direction of the electric field at the center of the square of length side 5cm , and q= 1x10-8 C, at its corners? +q -2q -q +2q 13 Dr. Emad Sayed  “‫”الخطوة األولى‬ +q2 -q1 +q2 -q1 E1 -q3 +q4 -q3 +q4 +q2 -q1 E1 E2 14 Dr. Emad Sayed -q3 +q4  “‫”الخطوة الثانية‬ (r1)2 = (2.5)2 + (2.5)2 r1 = 3.5 cm = 3.5x10-2 m +q2 -q1 E4 E1 r1 = r2 = r3 = r4 q1 = -2x10-8 C E3 E2 q2 = +1x10-8 C q3 = -1x10-8 C -q3 +q4 q4 = +2x10-8 C -q1 r1 2.5 cm E1=144x103 N/C , E2=72x103 N/C E3=72x103 N/C , E4=144x103 N/C 2.5 cm 15 Dr. Emad Sayed  “‫”الخطوة الثالثة‬ +q2 -q1 E4 E1 -q1 E1 E3 θ E2 θ1 = θ2 = θ3 = θ4 = 45o -q3 +q4 E1x=E1 cos45 =102x103 N/C E1y=E1 sin45 =102x103 N/C E2x=E2 cos45 =51x103 N/C E2y=-E2 sin45 =-51x103 N/C E3x=-E3 cos45 =-51x103 N/C E3y=-E3 sin45 =-51x103 N/C E4x=-E4 cos45 =-102x103 N/C E4y=E4 sin45 =102x103 N/C Ex= 0 Ey=102x103 N/C E=102x103 N/C in the +ve y-direction 16 Dr. Emad Sayed  Note The resultant field of two charges equals zero only if: 1- r = 2- The two fields are equal in magnitude and opposite in direction. 17 Dr. Emad Sayed  Example Determine the zone at which the electric field may equal to zero in the following cases: a. A +q1 B +q2 C b. A -q1 B +q2 C 18 Dr. Emad Sayed  a. A +q1 B +q2 C E1 +q1 E2 +q2 E2 E1 A +q1 B +q2 C (E) never equals zero in zone A 19 Dr. Emad Sayed  E2 E1 A +q1 B +q2 C (E) never equals zero in zone C E2 E1 A +q1 B +q2 C (E) may equal to zero in zone B 20 Dr. Emad Sayed  b. E1 E2 A -q1 B +q2 C (E) may equal to zero in zone C E2 E1 A -q1 B +q2 C (E) may equal to zero in zone A E1 E2 A -q1 B +q2 C (E) never equals zero in zone B 21 Dr. Emad Sayed  Example Locate the points at which the electric field equals zero in the following cases: a. +5 μC +1 μC 2m b. -5 μC +1 μC 2m 22 Dr. Emad Sayed  a. E2 E1 q1 = 5x10-6 C q2 = 1x10-6 C +q1 +q2 E1 = E2 2-x x 5x2 = (2-x)2 x = 0.6 m and X=∞ 23 Dr. Emad Sayed  b. The point is chosen q1 = -5x10-6 C nearer to smaller charge value q2 = 1x10-6 C E1 E2 E1 = E2 -q1 +q2 x 2+x 5x2 = (2+x)2 x = 1.6 m and X=∞ 24 Dr. Emad Sayed  To Remember Origin of charge Coulomb's law Electric field Superposition of electric field 25 Dr. Emad Sayed