Electric Charges and Fields Electrostatics Branch of physics that deals with apparently stationary electric charges and the forces exerted by unchanging electric fields on charged objects Charge Property associated with a particle/body due to which it can produce electric or magnetic effects • Two types of charges, positive and negative • Like charges repel and opposite charges attract • Excess or deficiency of electrons is responsible for net charge • Always associated with mass, if body gains a net negative charge, its mass slightly increases • SI unit of charge: Coulomb (C) with dimensions [AT] Quantization of charge Charge on any body is an integral multiple of the minimum charge • If q is the charge on a body, π = ±ππ • π = π. π × ππ–ππ πͺ π∈β€ • e is known as fundamental/elementary charge • e is the charge carried by 1 proton or 1 electron Law of conservation of charge Charge can neither be created nor be destroyed, but can only be transferred from one body to another (or) total net charge of an isolated physical system always remains constant Electrification Methods of charging a body 1) Friction When 2 bodies are rubbed, both acquire some charge with one gaining a net positive and the other gaining a net negative • glass rod + silk → glass rod+ and silk2) Conduction When a neutral conductor comes in contact with a charged conductor, charge flows into the neutral body and gets charged • Same polarity is seen in both bodies 3) Induction When a charged body is brought near a neutral body without touching it, charges are developed on the uncharged body • Opposite polarity is induced When a charged metal sphere is grounded, electrons either flow to the ground or from the ground depending on the charge of the region where connection has been made Coulomb’s Law Electrostatic force of attraction or repulsion between 2 point charges is directly proportional to the product of their changes and inversely proportional to the distance between them squared πΉ=π • Where π = 1 4ππ0 π1 π2 π2 known as the Coulomb’s Law constant • For air or vacuum where π0 = 8.857 × 10−12 π = 9 × 109 ππ2 πΆ2 ππ2 , πΆ2 • F12 is force ON 1 exerted BY 2, F21 is force ON 2 exerted BY 1 • r12 is TOWARDS 1 from 2, r21 is TOWARDS 2 from 1 • πβββββ π1 − βββ π2 12 = βββ π21 = βββ βββββ π2 − βββ π1 If the position vector of two charges q1 and q2 are βββ π1 and βββ π2 , the electrostatic force on charge q1 due to q2 is, βββββ πΉ12 = 1 π1 π2 (πβββ − βββ ⋅ π2 ) 4ππ0 |πβββ1 − βββ π2 |3 1 βββββ πΉ12 = 1 π1 π2 ⋅ πΜ 4ππ0 |πβββ1 − βββ π2 |2 12 If the position vector of two charges q1 and q2 are βββ π1 and βββ π2 , the electrostatic force on charge q2 due to q1 is, ββββββ πΉ21 = 1 π1 π2 (πβββ − βββ ⋅ π1 ) 4ππ0 |πβββ2 − βββ π1 |3 2 ββββββ πΉ21 = 1 π1 π2 ⋅ πΜ 4ππ0 |πβββ2 − βββ π1 |2 21 Coulomb’s Law in vector notation Here both charges are equal, and the force exerted by each on the other are equal and opposite βββββ ββββββ πΉ 12 = −πΉ21 Electrostatic force between >2 charges The total force on a charge q1 can be calculated by vector addition as, or using the formula βββββ πΉ12 + βββββ πΉ13 = 2 2 √πΉ12 + πΉ21 + 2 ⋅ πΉ12 ⋅ πΉ21 ⋅ cos π Principle of superposition In a system of charges from q1 to qn, the force on q1 due to q2 is the same as given by Coulomb’s Law, i.e., its effect is not altered by the presence of other charges • Rather, they all exert their own forces on q1 and thereby alter the net force on q1 • This net force is the vector sum of all the forces exerted by each of the other charges on q1 Test charge A very small/point positive charge that doesn’t affect the other charges, using which we can determine the effect of those other charges Electric field Space around an electric charge where its effect is felt Electric field lines Imaginary pictorial representations showing the path a test charge would take in an electric field • Start from positive charges and end at negative charges • In an isolated positive charge, lines are radially outward • In an isolated negative charge, lines are radially inward • Tangent at any point of a field line gives the direction of field • They can never intersect Electric field intensity Force experienced by a unit positive (test) charge placed at that point πΈ = πΉ⁄π π πΈ = πΜ Μ Μ π2 • A charge in an electric field experiences a force whether it is at rest or moving • The electric force is independent of mass and velocity of the charged particle, but only the charge • Intensity of electric field is a vector quantity. Its direction is always away from the positive charge and towards the negative charge • SI unit is newton per coulomb with dimensions [MLT-3A-1] • In vector form, 1 π ⋅ 3π 4ππ0 π • If instead of a single charge, field is produced by many charges, πΈβ = the resultant electric field intensity is • If the test charge is positive, then the force acting on it is in the direction of the field • If the test charge is negative, the force acting on it is in the opposite direction of the field Electric fields and multiple charges • If two equal and opposite charges are separated by a distance d, ββββ1 + πΈ ββββ2 E at the midpoint of line joining them is πΈβ = πΈ πΈβ = 1 8π ⋅ 4ππ0 π 2 • If two equal charges are separated by distance d, electric field intensity at the midpoint is zero • Two charges +Q each are placed at the two vertices of an equilateral triangle of side a. The intensity of electric field at the third vertex is • Two charges +Q, –Q are placed at the two vertices of an equilateral triangle of side ‘a’, then the intensity of electric field at the third vertex is • If three charges +Q each are placed at the three vertices of an equilateral triangle of side ‘a’ then the intensity of electric field at the centroid is zero
