MATTER CHARGE COULOMB s LAW and the ELECTRIC FIELD MATTER CHARGE a A neutral object is charged to 1 0 mC Are electrons transferred to or from the object Determine the NUMBER OF ELECTRONS TRANSFERRED during the charging process m 10 3 ANS n Q e 6 25x1015 electrons TRANSFERRED FROM object b Consider two IDENTICAL conductors C1 and C2 where Q1 2 0 C and Q2 4 C C1 and C2 are placed in contact then separated determine the FINAL CHARGE on each conductor and the NUMBER OF ELECTRONS TRANSFERRED from C2 to C1 e 1 6x10 19 C ANS Q1 Q2 Q1 Q2 Conservation of CHARGE and for IDENT ICAL CONDUCTORS Q1 Q2 1 C n Q1 e 1 88x1013 electrons transferred from C2 to C1 222 a gaseous radioactive ISOTOPE of Radon poses a c Rn86 potential health hazard Determine the NUCLEAR COM POSITION Z N A of this isotope the NUCLEAR CHARGE and NET ATOMIC CHARGE associated with a single atom of Rn86 ANS Z 86 protons N A Z 136 neutrons 222 NUCLEONS QNUCLEUS 86e QATOM 0 222 d Determine the TOTAL NUMBER of ELECTRONS the TOTAL NUMBER of PROTONS the TOTAL NUMBER of NEUTRONS and finally the NET CHARGE associated with a 27 g sample of SILVER Ag47 M 108 g mole AVOGADRO s number 6 025x1023 particles mole e 1 6x10 19 C ANS 27 g represents 0 25 molecules of Ag47 1 51x1023 ATOMS TOTAL PROTONS 47 1 51x1023 7 08x1024 TOTAL ELECTRONS TOTAL NEUTRONS 108 47 1 51x1023 9 19x1024 NET CHARGE 0 108 ATOMS or 108 The H2 ION In a simplified MODEL of the H2 single shared electron as diagrammed below s 1 Ao qproton 1e qelectron 1e 1 Ao 1x10 10 m e 1 6x10 19 C ION two protons flank a a Determine the NET ELECTROSTATIC FORCE on the ELECTRON ANS Fe F1 e F2 e 0 N b Determine the NET ELECTROSTATIC FORCE separately on each of the PROTONS and indicate on the DIAGRAM the DIRECTION of the NET FORCE on each of the PROTONS ANS Fp Fe p Fp p Fp 1 73x10 8 N COULOMB s LAW Fj 0 k qj q0 Rj 0 2 F0 Fj 0 Consider an array of SOURCE CHARGES Q1 Q 0 a 0 Q2 Q 0 a 0 Q3 Q a 0 0 Q4 Q a 0 0 where Q 1 C a 0 01 m 1x10 6 k 9x109 Nm2 C2 Determine the NET ELECTROSTATIC FORCE DIRECTION and MAG NITUDE on a TEST CHARGE q0 0 1 C located at 0 0 0 Determine the DIRECTION of the NET ELECTROSTATIC FORCE on the TEST CHARGE q0 0 1 C located at 0 0 a F1 0 kQq0 R2 u F0 F1 0 F2 0 Consider a DIPOLE situated and oriented as indicated in the diagram Show that the ELECTRICAL FORCE on a POSITIVE TEST CHARGE q0 located at a position x 0 x s F0 4kQq0sx x2 s2 2 ux The ROLE of the SOURCE CHARGE DISTRIBUTION Consider the following CHARGE DISTRIBUTION where the CHARGE Q Q Q Determine the DIRECTION of the ELECTRICAL FORCE on a POSITIVE TEST CHARGE q0 located at the FIELD POINT 0 s due to the CHARGE DISTRIBUTION when a Q Q b Q Q 2 c Q 0 d Q Q 2 e Q Q F0 dF0 Consider the continuous LINEAR CHARGE DISTRIBUTION situated and oriented as indicated Length L linear charge density Determine the GENERAL EXPRESSION for the ELECTROSTATIC FORCE on a POSITIVE TEST CHARGE q0 located at a POSITION 0 y due to the LINEAR SOURCE CHARGE DISTRIBUTION SHOW ALL steps in a clear and organized manner The ELECTROSTATIC DEFLECTOR An electron BEAM enters the ELECTROSTATIC DEFLECTOR at 0 0 initial VELOCITY V0 5x106 m s 0 qe e me 9 11x10 31 kg L 0 010 m PLATE SEPARATION s 0 006 m Determine the ELECTRIC FIELD Ey for which the ELECTRON BEAM just CLEARS the TOP DEFLECTOR PLATE QUESTIONS 1 and 2 refer to the QUADRAPOLAR CHARGE distri bution sketched in the accompanying DIAGRAM 1 The DIRECTION of the ELECTRIC FIELD due to the CHARGE DISTRIBUTION at POSITION a A B C D E 0 2 The DIRECTION of the ELECTRIC FIELD due to the CHARGE DISTRIBUTION at POSITION b A B C D E 0 The DIPOLE ELECTRIC FIELD A DIPOLE CHARGE DISTRIBUTION is oriented and positioned as diagrammed below Q e s 2Ao 1 Ao 1x10 10 m e 1 6x10 19 C k 9x109 N m2 C2 a What is the DIRECTION of the DIPOLE ELECTRIC FIELD at FIELD POSITION a b c d ANS a b c d b Determine the DIPOLE ELECTRIC FIELD MAGNITUDE and DIRECTION at FIELD POINT a ANS Ea 2 70x1010 N C c Determine the DIPOLE ELECTRIC FIELD MAGNITUDE and DIRECTION at FIELD POINT b ANS Eb 2 70x1010 N C d Determine the NET ELECTROSTATIC FORCE MAGNITUDE and DIRECTION on a NEGATIVELY CHARGED ION q0 2e at FIELD POSITION a ANS F0 q0Ea 8 64x10 9 N C E dE kdQ R2 u Consider a thin semi circular insulator carrying a uniform linear charge density radius b The orientation of the insulator in indicated in the diagram center 0 0 0 Determine the ELECTRIC FIELD at FIELD POSITIONS 0 0 0 and 0 0 z where z 0 NOTE k 9x109 N m2 C2 b 0 10 m 1x10 6 C m
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