HUE AI Physics Lecture 2, Fall 2024-2025 PDF

Physics BAS-101 First Level Fall Semester 2024-2025 1 By Ass. Prof. M...

Physics BAS-101 First Level Fall Semester 2024-2025 1 By Ass. Prof. Mohamed Abdelghany Dr. Nermin Ali Abdelhakim Dr. Enas lotfy Faculty of AI , Level 1, Physics, Lecture 2  2 Foundations of Electricity Faculty of AI , Level 1, Physics, Lecture 2 3 Every object contains a vast amount of electric charge. Electric charge can be either positive or negative. Charges with the same electrical sign repel each other, and charges with opposite electrical signs attract each other. An object with equal amounts of the two kinds of charge is electrically neutral, whereas one with an imbalance is electrically charged or net charged. 4 Charged objects interacts by exerting forces on one another (by transformation of charge from one object to another). So, when a glass rod is rubbed with silk, the glass losses some of its negative (electrons) charge and then has a unbalanced positive charge And when the plastic rod is rubbed with fur, the plastic gains a unbalanced negative charge (electron). 5  CONDUCTORS AND INSULATORS 6 Material can be classified according to the ability of charge to move through them. Materials classified to: 1. Conductor: materials through which charges can move freely, such as metal. 2. Insulators: materials in which charges cannot move freely, such as rubber, plastic, glass. 3. Semiconductors: materials that are intermediate between conductors and insulator, such as silicon, germanium. 4. Superconductors: materials that are perfect conductors where charge move without any resistance.  CURRENT AND RESISTANCE 7 We study the flow of electric charges through a piece of material. The amount of flow depends on both the material through which the charges are passing and the potential difference across the material. Whenever there is a net flow of charge through some region, an electric current is said to exist. 8 To define current more precisely, suppose charges are moving perpendicular to a surface of area A as shown in Figure.  9 ❖The current is defined as the rate at which charge flows through this surface. ❖If ∆Q is the amount of charge that passes through this surface in a time interval ∆t, the average current Iavg is equal to the charge that passes through A per unit time: ∆𝑸 𝑰𝒂𝒗𝒈 = ∆𝒕  10 If the rate at which charge flows varies in time, the current varies in time; we define the instantaneous current I as the differential limit of average current as ∆t → 0: 𝒅𝑸 𝑰𝒂𝒗𝒈 = 𝒅𝒕 ❑The SI unit of current is the ampere (A): 1 A = 1 C/s. That is, 1 A of current is equivalent to 1 C of charge passing through a surface in 1 s. 11 ❑ It is conventional to assign to the current the same direction as the flow of positive charge. ❑ In electrical conductors such as copper or aluminum, the current results from the motion of negatively charged electrons. ❑ Therefore, in an ordinary conductor, the direction of the current is opposite the direction of flow of electrons.  12 ▪ Consider the current in a cylindrical conductor of cross-sectional area A. ▪ The volume of a segment of the conductor of length ∆x (between the two circular cross sections shown in Figure, is (A ∆x). ▪ If n represents the number of mobile charge carriers per unit volume (in other words, the charge carrier density), ▪ the number of carriers in the segment is:(nA ∆x). Therefore, the total charge ∆Q in this segment is: ▪ ∆Q=(nA ∆x) q ▪ where q is the charge on each carrier.  13 If the carriers move with a velocity vd (drift velocity) parallel to the axis of the cylinder, the magnitude of the displacement they experience in the x direction in a time interval ∆t is ∆x = vd ∆t. we can write ∆Q as: ∆𝑸 = 𝒏𝑨𝒗𝒅∆𝒕 𝒒 Dividing both sides of this equation by ∆t, we find that the average current in the conductor is: ∆𝑸 𝑰𝒂𝒗𝒈 = = 𝒏𝒒𝒗𝒅𝑨 ∆𝒕  CURRENT DENISTY 14 Sometimes we are interested in the current i in a particular conductor. At other times we take a localized view and study the flow of charge through a cross section of the conductor at a particular point. To describe this flow, we can use the current density J, which has the same direction as the velocity of the moving charges if they are positive and the opposite direction if they are negative.  15 Consider a conductor of cross-sectional area A carrying a current I. The current density J in the conductor is defined as the current per unit area. Because the current I = nqvdA, the current density is: 𝑰 𝑱= = 𝒏𝒒𝒗𝒅 𝑨 Where A is the total area of the surface. So, we see that the SI unit for current density is the ampere per square meter (A/ m2).  Now, it is possible to rewrite the draft velocity as in the form: 16 𝐢 𝐉 𝐯𝐝 = = 𝐧𝐀𝐪 𝐧𝐪 where J has SI units of amperes per meter squared. This expression is valid only if the current density is uniform and only if the surface of cross-sectional area A is perpendicular to the direction of the current. In some materials, the current density is proportional to the electric field: 𝑱 = 𝝈𝑬 where the constant of proportionality σ is called the conductivity of the conductor.  OHM'S LAW 17 ❑ We can obtain an equation useful in practical applications by considering a segment of straight wire of uniform cross- sectional area A and length ℓ, as shown in Figure. ❑ A potential difference ∆V = Vb - Va is maintained across the wire, creating in the wire an electric field and a current. ❑ If the field is assumed to be uniform, the potential difference is related to the field through: ∆V=Eℓ.  18 Therefore, we can express the current density in the wire as: ∆𝑽 𝑱 = 𝝈𝑬 = 𝝈 𝓵 𝑰 Because 𝑱 = , the potential difference across the wire is: 𝑨 𝓵 𝓵 ∆𝑽 = 𝑱 = 𝑰 = 𝑹𝑰 𝝈 𝝈𝑨 𝓵 The quantity 𝑹 = is called the resistance of the conductor. 𝝈𝑨  19 We define the resistance as the ratio of the potential difference across a conductor to the current in the conductor: ∆𝑽 𝑹= 𝑰 This result shows that resistance has SI units of volts per ampere. One volt per ampere is defined to be one ohm (𝜴): 𝟏 𝜴 = 𝟏𝑽/𝑨 The inverse of conductivity is resistivity ρ: ρ= 1/σ where ρ has the units (ohm. meters) (Ω/ m).  20 𝓵 Because 𝑹 = , we can express the resistance of a uniform 𝝈𝑨 block of material along the length, as: 𝓵 𝑹=𝝆 𝑨 ✓ Every ohmic material has a characteristic resistivity that depends on the properties of the material and on temperature. ✓ In addition, the resistance of a sample depends on geometry as well as on resistivity.  COULOMB’S LAW 21 The force of repulsion or attraction between two pair charges (q1 and q2) separated by a distance ( r ) from each other is given by: 𝒒𝟏 𝒒𝟐 𝟏 𝒒𝟏 𝒒𝟐 ഥ = 𝑲𝒆 𝑭 = 𝒓 𝟐 𝟒𝝅𝜺𝒐 𝒓𝟐  22 𝟏 𝟗 𝒎𝟐 Where 𝑲𝒆 : is constant equal = = 𝟖. 𝟗𝟗 𝒙𝟏𝟎 𝑵. 𝟒𝝅𝜺𝒐 𝒄𝟐 𝜺𝒐 = 𝟖. 𝟖𝟓 × 𝟏𝟎 𝒄 /𝑵. 𝒎𝟐 𝟏𝟐 𝟐 and 𝑞1 𝑎𝑛𝑑 𝑞2 is the charges in coulomb unit c. If we have (n) charged particle they interact independently in pairs, and the force on any one of them is given by: 𝑭𝟏𝒏𝒆𝒕 = 𝑭𝟏𝟐 + 𝑭𝟏𝟑 + 𝑭𝟏𝟒 + ⋯ + 𝑭𝟏𝒏  Charge is quantized and conserved 23 Electrical fluid is not continuous but is made up of multiples of certain elementary charge, where any charge (+ or -) can be detected and written in the form: 𝒒 = 𝒏𝒆 , where n= ±1, ±2, … and e = 1.602x10-19 C. When a physical quantity, such as charge, can have only discrete values, we say that this quantity is quantized. Also, electric charge is conserved, where the net charge of any isolated system cannot change. This means that charges not created but only transfers from one body to another.  ELECTRIC FIELD 24 While we need two charges to quantify the electric force, we define the electric field for any single charge distribution to describe its effect on other charges. In principle, we can define the electric field at some point near the charged object, such as point P. We first place a positive charge qo called a test charge, at the point. We then measure the electrostatic force F that acts on the test charge.  25 Finally, we define the electric field E at point P due to the charged object as: ഥ 𝑭 ഥ= 𝑬 𝒒𝒐 This equation gives us the force on a charged particle qo placed in an electric field. If q is positive, the force is in the same direction as the field. If q is negative, the force and the field are in opposite directions. 26 27 28