ASRJC Electric Field Notes

ANDERSON SERANGOON JUNIOR COLLEGE PHYSICS 9749 Additional Notes Topic 13 Electric Fields Content A Concept of an electric field B Electric force between point charges C Electric field of a point charge D Uniform electric fields E Electric potential Learning Outcomes Candidates should be able to: (a) show an understanding of the concept of an electric field as an example of a field of force and define electric field strength at a point as the electric force exerted per unit positive charge placed at that point. (b) represent an electric field by means of field lines. (c) recognise the analogy between certain qualitative and quantitative aspects of electric and gravitational fields. (d) recall and use Coulomb’s law in the form 2 21 04 1 r QQF = for the force between two point charges in free space or air. (e) recall and use E = 2 04 1 r Q  for the field strength of a point charge in free space or air. (f) calculate the electric field strength of the uniform field between charged parallel plates in terms of potential difference and plate separation. (g) calculate the forces on charges in uniform electric field. (h) describe the effect of a uniform electric field on the motion of charged particles. (i) define electric potential at a point as the work done per unit positive charge in bringing a small test charge from infinity to that point. (j) state that the field strength of the field at a point is numerically equal to the potential gradient at that point. (k) use the equation 04 QV r= for the electric potential in the field of a point charge, in free space or air. Name: ________________________________ ( ) Class: 25 / ___

ANDERSON SERANGOON JUNIOR COLLEGE PHYSICS 9749 13-2 Additional Notes A Concept of an electric field Candidates should be able to: (a) show an understanding of the concept of an electric field as an example of a field of force and define electric field strength as force per unit positive charge. (b) represent an electric field by means of field lines. A.1 Concept of an electric field: Many everyday forces are pushes or pulls between bodies in contact. In other cases forces arise between bodies that are separated from one another (action- at-a-distance forces). An action-at-a-distance effect in which one body A exerts a force on another body B not in contact with it, can be regarded as due to a 'field of force' (or simply field) in the region around A. Field of force is a region of space where a body experiences a force. A.2 Definition of electric field: An electric field is a region of space where a stationary charge experiences a force. The direction of the electric field is the direction of the force on a positive charge. Note: The definition is in terms of the force on a stationary charge. A force on a moving charge could indicate that a magnetic field is present. A.3 Electric field strength (intensity), E: Electric field strength at a point is defined as the force per unit positive charge acting on a small stationary charge placed at that point. FE q= where F is the force acting on a small stationary positive charge, q. Units: N C-1 or V m-1 E is a vector quantity. To standardise: the direction of field to be drawn as the direction of force on a positive test charge. F q (+ve charge) E F q (-ve charge) E Later you will learn that a magnetic field can cause a force to act on a moving charge. The test charge must be small so that the E- field will not be distorted. Compare E with gravitational field strength memorize

ANDERSON SERANGOON JUNIOR COLLEGE PHYSICS 9749 13-3 Additional Notes A.4 Representing an electric field: An electric field can be represented and so visualised by electric field lines (lines of force). Electric field lines are lines that show the direction of the force acting on a stationary positive point charge in the field. The field line is imaginary but the field it represents is real. Examples: (a) Isolated point charge: (b) Electric dipole: The electric field lines originate on the positive charge and end on the negative charge. A positive test charge will experience two forces when placed at point A. The resultant of these two forces is tangent to the line of the force at A. (c) Uniform electric field: The battery places equal charges of opposite sign on the two metal plates. Although some “fringing” of the lines occurs near the edges, the field lines are mostly directed straight across the gap between the plates. The electric field between the plates is uniform. This is indicated in the diagram by the equal spacing of the field lines.

ANDERSON SERANGOON JUNIOR COLLEGE PHYSICS 9749 13-4 Additional Notes (d) Two like charges: The stronger the electric field is, the closer the lines of force. The field is weak midway between the charges. (e) Metal conductors: The The electric field just outside the surface of a metal is perpendicular to the surface. A.5 Summary of the rules for drawing electric lines of force around electrically charge bodies: Rule Diagram 1 Electric lines of force always leave +ve charges and end on -ve charges. A.4 (b) 2 Field lines always leave (or end on) conducting surfaces at right angles to the point of contact. A.4 (e) 3 A uniform electric field has equally spaced field lines. A.4 (c) 4 The stronger the electric field around a charged body, the closer the lines of force. A.4 (d) 5 Field lines never cross. A.4 (a) to (e)

ANDERSON SERANGOON JUNIOR COLLEGE PHYSICS 9749 13-5 Additional Notes Check Your Understanding 1 Consider the four field patterns shown. Assuming there are no charges in the regions shown, which of the pattern represents a possible electrostatic field? Check Your Understanding 2: A charged sphere has both a gravitational field and an electric field around it. The diagram represents the field around such a sphere. Which field could this diagram represent ? A both electric and gravitational B electric but not gravitational C gravitational but not electric D neither electric nor gravitational [2013 P1 Q24] B A C D

ANDERSON SERANGOON JUNIOR COLLEGE PHYSICS 9749 13-6 Additional Notes A.6 Electric field in daily life: Lightning Explore the cause of lightning and the use of lightning conductors, which serve to protect lives, properties and equipment. B Electric force between point charges: Candidates should be able to: (d) recall and use Coulomb's law in the form 2 21 04 1 r QQF = for the force between two point charges in free space or air. B.1 Coulomb's law: The force between two point charges Q1 and Q2 is directly proportional to the product of the charges and inversely proportional to the square of the distance r between them. 2 21 r QQkF = where k is a constant or 2 21 04 1 r QQF = where 0 (epsilon naught): permittivity of free space (vacuum or air)=8.8510−12 C2 N−1 m−2 B.2 Direction of electrostatic force: The direction of the electrostatic force is along the line joining the two charges. (a) The force is repulsive if Q1 and Q2 are charges of the same signs. (b) The force is attractive if Q1 and Q2 are charges of opposite signs. Q1 Q2 − Q1 + Q2 Compare with gravitational force F F F F Compare with Newton’s Law of Gravitation.

ANDERSON SERANGOON JUNIOR COLLEGE PHYSICS 9749 13-7 Additional Notes Worked Example (a) Find the force of the electrostatic repulsion between 2 protons, a distance of 110−15 m a