ELECTRIC CHARGES AND FIELDS Introduction Electric charges are a fundamental concept in physics and they play a crucial role in our daily lives From the static electricity that makes your hair stand on end to the intricate electronics in our devices electric charges are everywhere In this chapter we ll explore the properties of electric charges how they interact with each other and the fields they create Basic Properties of Electric Charges Electric charges come in two varieties positive and negative Just like with magnets opposite charges attract each other while like charges repel each other The fundamental unit of electric charge is the coulomb C and the charge of a single proton or electron is 1 6 x 10 19 C One important property of electric charges is that they are conserved This means that the total amount of charge in a closed system remains constant over time Another property is that charges can be quantized meaning that they come in discrete amounts rather than continuously variable amounts Coulomb s Law F k q1 q2 r 2 The force between two point charges is given by Coulomb s law where F is the force k is a constant approximately 8 99 x 10 9 N m 2 C 2 q1 and q2 are the charges and r is the distance between them Example of two charged spheres being repelled by each other We can calculate the force of repulsion using Coulomb s law Let s say the charges on the spheres are 2 C and 3 C and they are separated by a distance of 0 1 m The force of repulsion is F 8 99 x 10 9 N m 2 C 2 2 x 10 6 C 3 x 10 6 C 0 1 m 2 F 5 394 x 10 3 N So the force of repulsion is about 0 54 N Electric Fields An electric field is a region around a charged particle or object within which other charges experience a force The electric field is a vector field meaning that it has both a magnitude and a direction at every point in space We can visualize the electric field using electric field lines The direction of the electric field is tangent to the electric field line at any point in space The density of the electric field lines indicates the strength of the electric field Example of calculating the electric field due to a point charge The electric field E at a distance r from a point charge Q is given by E k Q r 2 where k is the same constant as in Coulomb s law Let s say we have a point charge of 5 C and we want to calculate the electric field at a distance of 0 2 m The electric field is E 8 99 x 10 9 N m 2 C 2 5 x 10 6 C 0 2 m 2 E 1 07375 x 10 6 N C So the electric field is about 1 07 MN C Electric Potential Electric potential is a scalar quantity that measures the electric potential energy per unit charge It is defined as the work done per unit charge to bring a charge from infinity to a specific point in an electric field The electric potential V at a point in an electric field is given by V k Q r where k is the same constant as in Coulomb s law and Q is the charge causing the electric field Example of calculating the electric potential due to a point charge Let s say we have a point charge of 3 C and we want to calculate the electric potential at a distance of 0 1 m The electric potential is V 8 99 x 10 9 N m 2 C 2 3 x 10 6 C 0 1 m V 2 697 x 10 6 V So the electric potential is about 2 697 MV Conductors and Insulators Conductors are materials that allow charge to flow easily while insulators are materials that do not allow charge to flow easily For example metals are good conductors because they have free electrons that can move around easily On the other hand materials like plastic and rubber are good insulators because they have tightly bound electrons that don t move around easily When you rub two different materials together electrons can be transferred from one material to the other leaving one material with a positive charge and the other with a negative charge This is called charging by friction For example if you rub a balloon on your hair the balloon will become negatively charged and your hair will become positively charged The force between two charged particles is given by Coulomb s law which states that the force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them The formula is Charging by Friction Coulomb s Law F k q1 q2 r 2 where F is the force q1 and q2 are the charges r is the distance between them and k is a constant of proportionality called Coulomb s constant For example if you have two point charges 3 C and 5 C and they are separated by a distance of 0 5 m the force between them can be calculated as F 9 x 10 9 N m 2 C 2 3 x 10 6 C 5 x 10 6 C 0 5 m 2 F 5 4 x 10 2 N This means that the force is attractive negative sign and has a magnitude of 0 054 N The electric field is a vector field that describes the force that a charged particle would experience at a given point in space The formula for the electric field due to a point charge is Electric Field E k q r 2 where E is the electric field q is the charge r is the distance from the charge and k is Coulomb s constant For example if you have a point charge of 5 C located at the origin of a coordinate system the electric field at a point 1 0 meters away can be calculated as E 9 x 10 9 N m 2 C 2 5 x 10 6 C 1 m 2 E 4 5 x 10 5 N C This means that a positive charge at 1 0 would experience a force of 4 5 x 10 5 N to the right Electric Potential V k q r The electric potential is a scalar field that describes the amount of electric potential energy per unit charge at a given point in space The formula for the electric potential due to a point charge is where V is the electric potential q is the charge r is the distance from the charge and k is Coulomb s constant For example if you have a point charge of 5 C located at the origin of a coordinate system the electric potential at a point 1 0 meters away can be calculated as V 9 x 10 …