Physics Lecture 3, BAS-101, Fall 2024-2025 (PDF)

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

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 3  2 Foundations of Electricity Faculty of AI , Level 1, Physics, Lecture 3  Electric Field lines 3 ❑ It is an imaginary line through the space around the charge. ❑ The relation between the field lines and electric field vectors are: At any point, the direction of a straight field line or the direction of the tangent to a curved field line gives the direction of E at that point  4 The field lines are drawn so that the number of lines per unit area, measured in a plane that is perpendicular to the lines, is proportional to the magnitude of E. Thus, E is large where field lines are close together and small where they are far apart. 5 ❑ Electric field lines extend away from positive charge (where they originate) and toward negative charge (where they terminate). The rules for drawing electric field lines are as follows: 6 ❖ The lines must begin on a positive charge and terminate on a negative charge. ❖ In the case of an excess of one type of charge, some lines will begin or end infinitely far away. ❖ The number of lines drawn leaving a positive charge. ❖ Approaching a negative charge is proportional to the magnitude of the charge. ❖ No two field lines can cross.  7 Because the charges are of equal magnitude, the number of lines that begin at the positive charge must equal the number that terminate at the negative charge. At points very near the charges, the lines are nearly radial, as for a single isolated charge. The high density of lines between the charges indicates a region of strong electric field.  The Electric Field Due to a Finite Number of Point Charge 8 9 The electric field at point P due to a group of source charges can be expressed as the vector sum 𝑞𝑖 𝐸ത = 𝐾𝑒 ෍ 2 𝑟𝑖 𝑖 where ri is the distance from the ith source charge qi to the point P. 10 ❖ If a charge Q is uniformly distributed throughout a volume V, the volume charge density 𝝆 is defined by: 𝑸 𝝆= 𝑽 where ρ has units of coulombs per cubic meter (C/m3). ❖ If a charge Q is uniformly distributed on a surface of area A, the surface charge density s (Greek letter sigma) is defined by: 𝑸 𝝈= 𝑨 Where σ has units of coulombs per square meter (C/m2).  11 ❖ If a charge Q is uniformly distributed along a line of length, the linear charge density l is defined by: 𝐐 𝛌= 𝐥 where 𝝀 has units of coulombs per meter (C/m).  Flux of an Electric Field 12 ❖ Consider an electric field that is uniform in both magnitude and direction as shown in Figure. ❖ The field lines penetrate a rectangular surface of area A, whose plane is oriented perpendicular to the field.  13 ❖ The number of lines per unit area (in other words, the line density) is proportional to the magnitude of the electric field. ❖ Therefore, the total number of lines penetrating the surface is proportional to the product EA. ❖ This product of the magnitude of the electric field E and surface area A perpendicular to the field is called the electric flux Ф𝑬 :  14 ❖ The value of ∆ФE depends both on the field pattern and on the Surface. ❖ By using the integration over a closed surface, we can write the net flux ∆ФE through a closed surface as: ❖ where En represents the component of the electric field normal to the surface.  Gauss's Law 15 In this section we describe a general relationship between the net electric flux through a closed surface (often called a gaussian surface) and the charge enclosed by the surface. This relationship, known as Gauss’s law. 16 ❖ Consider a point charge q surrounded by a closed surface of arbitrary shape. ❖ The total electric flux through this surface can be obtained by evaluating E.∆A for each small area element ∆A and summing over all elements. 17 18 ❖ The electric flux is independent of the shape of the closed surface and independent of the position of the charge within the surface. 19 20 21 22