RI Chap 14 Electric Fields Lecture Notes

14 ELECTRIC FIELDS H2 Physics 9478 Content Page 14.1 Coulomb’s Law 3 14.2 Electric Field Strength 6 14.3 Electric Potential Energy and Electric Potential 12 14.4 Important Relationships 19 14.5 Uniform Electric Fields 24 14.6 Conductors in Electrostatic Equilibrium 30 14.7 Capacitance and Capacitors 34 14.8 Electric Field & Gravitational Field: Comparison & Summary 41 14.9 Appendix 43 Learning Outcomes Candidates should be able to: (a) recall and use coulomb’s law in the form 12 2 0 1 4 QQF rπε= for the electric force between two point charges in free space or air. (b) recall and use 2 0 1 4 QE rπε= for the electric field strength due to a point charge, in free space or air, to solve problems. (c) define electric potential at a point as the work done per unit charge by an external force in bringing a small positive test charge from infinity to that point. (d) use the equation 2 0 1 4 QV rπε= for the electric potential in the field due to a point charge, in free space or air. (e) show an understanding that the electric potential energy of a system of two- point charges is 12 0 1 4 E QQU rπε= . (f) recall that electric field strength at a point is equal to the negative potential gradient at that point and use this to solve problems. (g) calculate the field strength of the uniform electric field between charged parallel plates in terms of the potential difference and plate separation. (h) calculate the force on a charge in a uniform electric field. [in H1 syllabus] (i) describe the effect of a uniform electric field on the motion of charged particles. [in H1 syllabus]

Page | 2 (j) define capacitance as the ratio of charge stored to the potential difference and use C QV= to solve problems. (k) recall that the electric potential energy stored in a capacitor is given by the area under the graph of potential difference against charge stored, and use this and the equations 1 2U QV= , 21 2 Q CU = and 2U CV= to solve problems.

RAFFLES INSTITUTION YEAR 56 PHYSICS DEPARTMENT Page | 3 14.1 Coulomb’s Law Charles Coulomb (1736–1806) measured the magnitudes of the electric forces between charged objects using the same torsion balance Cavendish used to meaure the value of the gravitational constant G (see Chapter 8). In 1785, he successfully overcame various obstacles after numerous experimentations and established the inverse- square law for electric force between charges which was analogous to Newton’s law of gravitation. The electric force between two point charges in free space or air is given by Coulomb’s law. https://www.aps.org/publication s/apsnews/201606/physicshisto ry.cfm where F is the magnitude of the electric force between point charges with charges 1Q and 2Q that are separated by a distance r. The constant of proportionality is 1 0(4 )πε − where 12 1 0 8.85 10 F mε −−= × is the permittivity of free space. NOTE • The electric forces that two poin