Electrostatic Force Lecture Notes PDF

Electrostatic Force Prepared by Dr. Amira Mofreh Electric Charges There are two kinds of charges in nature, which were given the names positive and negative. – The charge like the one of electrons is called negative and – The one like the charge of protons is called positive...

Electrostatic Force Prepared by Dr. Amira Mofreh Electric Charges There are two kinds of charges in nature, which were given the names positive and negative. – The charge like the one of electrons is called negative and – The one like the charge of protons is called positive. Charges of the same sign repel each other and charges of opposite signs attract each other. Electric Charges Electric charge is conserved. That is, charge is not created or destroyed. Electric charge is quantized. – That is, it can only assume quantum values. – These are multiples of a fundamental charge e = 1.60219 x 10-19 Coulomb. – This is the charge of the proton which is also the absolute value of the charge of the electron. Point Charge The term point charge refers to a particle of zero size that carries an electric charge. The electrical behavior of electrons and protons is well described by modeling them as point charges. Practically speaking any charged particle whose dimensions are negligible as compared to its distances from other particles can be considered to be a point charge.  The electron and proton are identical in the magnitude of their charge, but very different in mass. The proton and the neutron are similar in mass, but very different in charge.  Coulomb’s Law Coulomb’s law describes the experimental results for the force of interaction between two point charges at rest, as The forces acting between two stationary point charges are: inversely proportional to the square of the separation r between the charged particles.  Coulomb’s Law directly proportional to the product of the charges q1 and q2 on the two particles. attractive if the charges are of opposite signs and repulsive if they have the same sign. The forces act along the line joining the two point charges. Coulomb’s Law, Equation Mathematically, q1 q2 q1 q2 Fe = ke  r 2 4 o r 2 The SI unit of charge is the coulomb. ke is called the Coulomb constant. – ke = 8.9876 x 109 N.m2/C2 = 1/(4πeo) – eo is the permittivity of free space. – eo = 8.8542 x 10-12 C2 / N.m2 Vector Nature of Electrical Forces   F21  F12 Example 1 : The electron and proton of a hydrogen atom are separated (on the average) by a distance of approximately 5.3x10-11 m. Find the magnitude of the electrostatic force. e e (1.6 x10 19 C ) 2 Fe  ke 2  (8.99 x10 N.m / C ) 9 2 2 11 2 r 12 (5.3x10 m)  Fe  8.2 x108 N The Principle of Superposition of Electrostatic Forces: Coulomb’s law describes the forces between two point charges. To find the resultant force acting on one point charge due to a group of stationary point charges we need to apply the Principle of Superposition of Electrostatic Forces. Principle of Superposition of Electrostatic Forces states that the force on one point charge in the presence of a number of stationary point charges is the vector sum of the forces acting on the point charge due to each individual charge of the group as given by Coulomb’s law. The Principle of Superposition of Electrostatic Forces: F21  The resultant force on q1 is the vector sum of all the forces exerted r̂31 r̂21 q1 on it by other charges. r̂41 F41 + r41  For example, if four charges are F31 + q4 present, the resultant force on one of these equals the vector sum of r21 r31 the forces exerted on it by each of - q3 the other charges.     + q2 F1  F21  F31  F41 Example 2 : Find the resultant force y acting on q3 in the figure. F23 F13 a q2 - +q 3 a 2a x + q 1 a = 0.10 m, q1 = q3 = 5.0 mC, q2 = -2.0 mC Solution q1 q3 F13  ke  11N y ( 2a ) 2 F13 F23 q2 a q2 q3 - +q 3 F23  ke  9.0N a2 a 2a F3  F13  F23 x F3 y  F13 y  F23 y  F13 sin 45  0  7.9 N + q 1 F3 x  F13 x  F23 x  F13 cos 45  F23  1.1N  F3  (1.1iˆ  7.9 ˆj )N Example 3: Two identical small charged spheres, each having a mass of 3.0 x 10-2 kg hang in equilibrium as shown in figure. The length of each string is 0.15 m, and the angle θ is 5.0°. Find the absolute value of the charge on each sphere.  Solution F x  T sin   Fe  0 F y  T cos  mg  0 Eliminating T from the two equations  Fe  mg tan   2.6x10-2 N q2 From Coulomb's law: Fe  ke 2 4a  q  4.4 x108 C Example 4 : Three point charges lie along the x axis as shown in figure. The positive charge q1 = 15.0 mC is at x = 2.00 m, the positive charge q2 = 6.00 mC is at the origin, and the resultant force acting on q3 is zero. What is the x coordinate of q3.  Solution q1 q3 q2 q3  F13  ke and F23  ke (2.00  x) 2 x2 For the net force on q3 to be zero, then F13  F23 q1 q3 q2 q3 q 2 (2.00  x ) 2  q1x 2  ke  ke (2.00  x) 2 x2 This equation can be reduced to 3x 2  8 x  8  0 The two roots are: “x=0.775m" which is the location at which the net force on q3 is zero, Accepted and " x= - 3.44m" which is a location at which the two forces have equal magnitudes but are in the same direction, Refused Example 5: Three charged particles are arranged in a line, as shown. Calculate the net electrostatic force on particle 3 (the -4.0 μC on the right) due to the other two charges. F = -1.5 N (to the left). 19 Example 6: Calculate the net electrostatic force on charge Q3 shown in the figure due to the charges Q1 and Q2. F = 290 N, at an angle of 65° 20