Position and relative position vectors In electrodynamics we frequently encounter problems involving two points a source point where an electric charge is located a field point at which you are calculating the electric or magnetic field 2 2 2 distance from the origin 2 2 2 unit vector pointing radially outward Relative position vector vector from the source point to the field point 2 2 2 Electric charge The electron s charge is The proton has charge C harge is quantized The SI International System of Units unit of charge is the coulomb the fundamental quantum of electric charge 1 602 10 19 9 11 10 31 1 The magnitude of the charge contained in 6 212 1018 electrons Electrostatics all the source charges are stationary Coulomb s law action at a distance law Coulomb s law describes the electrostatic force or electric force between two charged particles If the particles have charges 1 and 2 are separated by distance and are at rest relative to each other then the force acting on each due to the other is given by 1 4 0 2 2 3 2 0 both charges are of the same sign is in the direction of The force is repulsive 0 the charges are of opposite sign is in the opposite direction to The force is attractive The electrostatic force is proportional to the product of the magnitude of the charges and inversely proportional to the square of the distance between them The unit vector shows that the force is parallel to the line joining the charges The constant 0 is called the permittivity of free space 0 8 85 10 12 2 2 10 7 2 by definition 8 99 109 2 2 by experiment Question equilibrium of two forces on a particle Systems of point charges points charges distributed at fixed positions 1 2 3 The electrostatic force obeys the principle of superposition Principle of superposition The interaction between any two charges is completely unaffected by the presence of others T o determine the force on test charge 1 force due to 1 2 force due to 2 the total force on will be given by the vector sum of the individual forces 1 1 2 1 3 1 4 0 2 2 2 3 2 Question A charge is placed at point Calculate the electrostatic force to which it is subjected 1 2 3 4 1 3 1 2 2 3 3 3 4 4 3 0 0 2 3 2 3 2 1 2 3 4 8 2 3 3 3 1 2 2 3 2 4 8 2 3 3 3 2 2 2 2 2 2 2 2 2 2 4 2 3 3 2 2 2 2 2 8 2 3 2 The Electric Field If we have several point charges 1 2 at distances 1 2 from the total force on is 1 2 1 4 0 1 1 2 1 2 2 2 2 4 0 1 1 1 2 2 2 2 2 1 4 0 1 2 1 2 3 sources of the field Physically is the force per unit charge that would be exerted on a test charge if you were to place one at Continuous distributions of charge point charges discrete distributions continuous charge distributions 4 0 2 Discrete distribution is the vector from the source charge to the field point Continuous distribution is the vector from therefore from or to the field point if the charge is spread out along a line linear charge density element of length 4 0 if the charge is smeared out over a surface surface charge density element of area if the charge fills a volume volume charge density element of volume 2 4 0 3 4 0 2 2 2 Uniform distribution of charge total charge If all the possibilities are simultaneously present from points from lines from surfaces from volumes