TJC 14 Electric Field

Unit 14: Electric Field LEARNING OUTCOMES Candidates should be able to: (a) recall and use Coulomb's law in the form 1 2 24 o Q QF r for the electric force between two point charges in free space or air. (b) recall and use 24 o QE r for the 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 4 o QV r 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 E o QQU r 1 21 4 . (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 forces on a charge in a uniform electric field. (i) describe the effect of a uniform electric field on the motion of a charged particle. (j) define capacitance as the ratio of the charge stored to the potential difference and use QC V 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 U QV1 2 , QU C 21 2 and U CV 21 2 to solve problems.

Unit 14: Electric Fields 2026 Temasek Junior College 2 1. 2 TYPES OF ELECTRIC CHARGES There are 2 types of electric charge – positive charge and negative charge. Using a simple model, we can consider matter to be made up of three types of particles: electrons (which have negative charge), protons (positive) and neutrons (neutral). An uncharged object has equal numbers of protons and electrons, net charge is zero. When one material is rubbed against another, there is friction between them, and electrons may be rubbed off one material onto the other. The material that has gained electrons is now negatively charged, and the other material is positively charged. It was observed that like charges repel and unlike charges attract each other. This shows that there exists an electric force of repulsion or attraction between two charges. The French physicist, Charles Coulomb (1738-1806), using a torsion balance of his own invention shown in the figure below , confirmed the existence of an inverse square law of the electric force. A Coulomb torsion balance On the basis of his experiments, he concluded that 1. the force F between two point charges Q1 and Q2 was directly proportional to the product of the two point charges. F ∝ Q1 x Q2 2. the force between the two point charges was inversely proportional to the square of the distance between them r2. F ∝ 1/r2 Combining the two equations give the Coulomb’s law of electric force described in the next section.

Unit 14: Electric Fields 2026 Temasek Junior College 3 2. COULOMB’S LAW Coulomb's Law states that the electri c force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of their separation. i.e. 1 2 2 Q QF r  For two charges Q1 and Q2 placed in vacuum (free space), we write Coulomb's Law as 1 2 2 1 Q QF = 4 roπε where oε4π 1 is the constant of proportionality and o is the permittivity of free space. The quantities o = 8.85 x 10-12 C2 N-1 m-2 (or F m-1) and oε4π 1 = 8.99 x 109 m F-1. Points to note: 1. If the charges are of the same sign, the force is repulsive and if the charges are of opposite sign, the force is attractive. 2. The electric forces which two charges exert on each other constitute an action - reaction pair. 3. The permittivity of air at s.t.p. is approximately equal to o. 4. The smallest unit of charge is the charge on an electron or proton which has an absolute value of e = 1.60 x 10-19 C. Since electric charge Q is quantized, we can write Q = Ne, where N is an integer.

Unit 14: Electric Fields 2026 Temasek Junior College 4 Example 1 Forces in a Hydrogen Atom The electron and proton of a hydrogen atom are separated by a distance of 5.3 x 10-11 m. Find the magnitudes of the (a) electric force between them, (b) gravitational force between them (c) ratio of the electric force to the gravitational force . Solution (a) Use Coulomb’s Law to find electric force. FE = r qq pe 24 1 επ o = )(5.3x10 ))(1.60x10(-1.60x10 x8.85x104 1 11- 2 -19-19 12- = -8.2 x10-8 N Note that the negative sign shows that it is an attractive force. (b) Use Newton’s law of gravitation to find the gravitational force. FG = G e p 2 m m r = 6.67 x 10-11 ).( ).)(.( 11 2731 1035 106711019   x xx 2 = 3.6 x10-47 N (c) The ratio of the 2 forces: G E F F = 2.27 x 1039 indicates that the electric force is a much stronger force and so the gravitational force between the charged constituents of the atom is considered negligible when compared with the electric force between them. Example 2 Three charges lie along the x-axis as shown in the figure. The positive charge q1 is 15 C at a distance x = 2.0 m from the positive charge q2 = 6.0 C. Where must a negative charge q3 be placed on the x-axis so that the resultant electric force acting on q3 is zero? + - proton electron Solution Let F13 and F23 be the attractive electric forces exerted by q1 and q2 on q3 respectively. Their magnitudes are F13 = )x0.2( 10x15 4 1 2 6   3q επ o F23 = x qx 4 1 2 3 6106  επ o Let the two forces cancel each other, F13 = F23 ).( x qx 4 1 2   02 1015 3 6 επ o = x qx 4 1 2 3 6106  επ o 6(2 - x)2 = 15x 2 Solving gives x = 0.77 m

Unit 14: Electric Fields 2026 Temasek Junior College 5 3. The Electric Field A charge Q sets up an electric field around it. This field is invisible but it can be detected by placing a small test charge q nearby. If this small charge q experiences a force even though they are not in contact, it provides evidence that charge Q sets up an electric field or `field of force' around it. An electric field E is said to exist at a region in space if a small charge q placed in it experiences an electric force. The electric field strength at a point is defined as the electric force per unit positive charge placed at that point. That is, E = F q Unit of E: N C-1 or V m-1 Note: 1. The electric field strength E is a vector quantity. 2. The direction of the electric field strength at any point is the same as the direction of the force experienced by a positive test charge placed at that point. Example 3 Electric Field strength A small charge q is placed in the electric field of a large charge Q. Both charges experience a force F. What is the electric field strength of the charge Q at the position of the charge q? A F Qq B F Q C Fq D F q F