Electrostatics I-Classical Physics-Handouts, Lecture notes of Classical Physics

Download Electrostatics I-Classical Physics-Handouts and more Lecture notes Classical Physics in PDF only on Docsity! PHYSICS –PHY101 VU © Copyright Virtual University of Pakistan 61 Summary of Lecture 22 – ELECTROSTATICS I 1. Like charges repel, unlike charges attract. But by how much? Coulomb's Law says that this depends both upon the strength of the two charges and the distance between them. In mathematical ter 1 2 1 22 2ms, which can be converted into an equality, . The constant of proportionality will take different values depending upon the units we choose. In the MKS system, charge is meas q q q qF F k r r ∝ = 0 12 2 2 9 2 2 0 1ured in Coulombs (C) and with 4 8.85 10 / and hence 8.99 10 / . 2. The situation is quite similar to that of gravity, except that electric charges and not masses are the sou k C Nm k Nm C πε ε − = = × = × 1 2 12 122 0 12 12 1 2 12 21 212 12 0 12 1 ˆrce of force. In vector form, is the force exerted by 2 on 1, 4 1ˆ ˆ where the unit vector is . On the other hand, is the force exerted 4 by 1 on q qF r r r q qr F r r r πε πε = = = 12 21 1 12 13 14 2. By Newton's Third Law, . For many charges, the force on charge 1 is given by, 3. Charge is quantized. This means that charge comes in certain units only. So th F F F F F F = − = + + + ⋅ ⋅ ⋅ ⋅ 19 e size of a charge can only be 0, , 2 , 3 , where 1.602 10 is the value of the charge present on a proton. By definition we call the charge on a proton positive. This makes the c e e e e C−± ± ± ⋅ ⋅ ⋅ ⋅ = × harge on an electron negative. 4. Charge is conserved. This means that charge is never created or destroyed. Equivalently, in any possible situation, the total charge at an earlier time is equal to the charge at a later time. For example, in any of the reactions below the initial charge = final charge: (electron and positron annihilate into neutral photons) e e γ γ− ++ → + 0 2 2 3 (neutral pion annihilates into neutral photons) (two deuterons turn into tritium and proton) 5. this a quantity that has a defin H H H p π γ γ→ + + → + Field : ite value at any point in space and at any time. The simplest example is that of a scalar field, which is a for any value of , , , . Examples: temperature inside a room ( , , single number x y z t T x y z, ) , density in a blowing wind ( , , , ), There are also which comprise of three numbers at each value of , , , . Examples: the velocity of wind, the pressure inside a fl t x y z t vector fields, x y z t ρ ⋅ ⋅ ⋅ uid, or even a sugarcane field. In docsity.com PHYSICS –PHY101 VU © Copyright Virtual University of Pakistan 62 1 2 3 every case, there are 3 numbers: ( , , , ) { ( , , , ), ( , , , ), ( , , , ) }. 6. The electric field is also an example of a vector field, and will be the most important for our purpose. V x y z t V x y z t V x y z t V x y z t= 0 0 It is defined as the force on a unit charge. Or, since we don't want the charge to disturb the field it is placed in, we should properly define it as the force on a "test" charge , . HFq E q ≡ 0 0 2 0 2 0 0 ere is very very small. The electric field due to a point charge can 1 be calculated by considering two charges. The force between them is and so 4 1 . A way to visualiz 4 q qqF r F qE q r πε πε = = = e E fields is to think of lines starting on positive charges and ending on negative charges. The number of lines leaving/entering gives the amount of charge. 7. Typical values for the maginitud 11 5 e of the electric field : Inside an atom- 10 N/C Inside TV tube- 10 N/C E 2 -2 In atmosphere- 10 N/C Inside a wire- 10 N/C 8. Measuring charge. One way to do this is to balance the gravitational force pulling a charged particle with mass m with the force exerted on it by a known electric field (see below). For equilibrium, the two forces must be equal and so . The unknown mg qE= charge can then be found from .mgq q E = 1 2 3 9. Given several charges, one can find the total electric field at any point as the sum of the fields produced by the charges at that point individually, or ii i i E E E E qE E k r = + + + ⋅ ⋅ ⋅ ⋅ ⋅ = =∑ ( )2 ˆ ˆ 1,2,3, . Here is the unit vector pointing from the charge to the point of observation. i i i r i r= ⋅ ⋅ ⋅∑ E eE mg y docsity.com