ch23 - The Electric Field Chapter Outline ENGINEERING...

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Unformatted text preview: The Electric Field Chapter Outline ENGINEERING PHYSICS II The Electric Field of Point Charges PHY 303L The Electric Field of Continuous Charge Distributions Lines of Electric Field Chapter 23: The Electric Field Motion in a Uniform Electric Field Electric Dipole in an Electric Field Maxim Tsoi Physics Department, The University of Texas at Austin http://www.ph.utexas.edu/~tsoi 303L: Electric Fields (Ch.22) 303L: Electric Fields (Ch.22) The Electric Field The Electric Field Field force Direction of electric field • The electric field vector E at a point in space is defined as the electric • A test charge q0 probes an electric field created by force Fe acting on a positive test charge q0 placed at that point divided by the test charge: a point charge q: r rF E≡ e q0 r q q0 ˆ Fe = k e 2 r r ⇒ r rF q ˆ E = e = ke 2 r q0 r • Electric field due to a group of source charges • The existence of an electric field is a property of its source equals the vector sum of the electric fields of all the charges: • E has the SI units of newtons per coulomb (N/C) r r Fe q ˆ E = ∑ i = ke ∑ i2 ri i q0 i ri • Force on a charged particle placed in an electric field: r r Fe = qE 303L: Electric Fields (Ch.22) 303L: Electric Fields (Ch.22) The Electric Field • Charge Density of a continuous charge distribution volume, surface, linear When the distances between charges in a group of charges is much • • To evaluate the resulting electric field: ρ= The system can be modeled as continuous • If a charge Q is uniformly distributed throughout a volume V, the volume charge density is smaller that the distance from the group to some point of interest • If a charge Q is uniformly distributed a surface of area A, surface charge density is 1) Divide the charge distribution into small elements with ∆q r ∆q ˆ ∆E = k e 2 r r r ∆q ˆ 3) Sum contributions of all elements E ≈ k e ∑ 2 i ri ri i 2) Calculate E due to ∆q r E = k e lim ∆qi → 0 ∆qi ∑r i i 2 ˆ ri = ke ∫ dq ˆ r r2 • If a charge Q is uniformly distributed along a line of length l, the λ= Q l If the charge is nonuniformly distributed over a volume, surface, or line, the amounts of charge dq in a small volume, surface, or length element are: dq = ρdV 303L: Electric Fields (Ch.22) the Q σ= A linear charge density is • Q V 303L: Electric Fields (Ch.22) dq = σdA dq = λ dl Example 3-5 1 Electric Field Lines Electric Field Lines convenient way of visualizing electric field patterns rules for drawing electric field patterns Introduced by Faraday draw curved lines that are parallel to the electric field vector at any point in space • The lines must begin on a positive charge and terminate on a negative charge. In the case of an excess of one type of • The electric field vector E is tangent to charge, some lines will begin or end infinitely far away the electric field line at every point. Direction of the line (indicated by • arrowhead) is the same as that of E • The number of lines drawn leaving (approaching) a positive (negative) charge is proportional to the magnitude of the The number of lines per unit area charge through a surface perpendicular to the lines is proportional to the magnitude of E. The lines are closer together • No two field lines can cross where E is stronger 303L: Electric Fields (Ch.22) 303L: Electric Fields (Ch.22) Electric Field Lines Electric Field Lines for a point charge for two point charges • • Positive point charge Two point charges of equal magnitude and opposite sign r q ˆ E = ke 2 r r • Negative point charge • • • Filed lines for +2q and –q electric Small pieces of thread suspended in oil align with the electric field charges and visualize the electric field lines • Two positive charges only the field lines that lie in the plane of figure are shown • 303L: Electric Fields (Ch.22) only the field lines that lie in the plane of figure are shown 303L: Electric Fields (Ch.22) Motion of Charge Particles • Motion of Charge Particles in a uniform electric field cathode ray tube (CRT) A particle of charge q and mass m in an electric field E is subject to electric force qE • Newton’s law r r r Fe = qE = m a ⇒ is commonly used to obtain a visual display of electronic information in oscilloscopes, radar systems, television receivers, computer monitors r r qE a= m • Electron beam is produced • The screen is coated with by an electron gun • The electric field between two oppositely charged plates is • material that emits visible approximately uniform light when bombarded with electrons Consider an electron is projected horizontally into this field with initial velocity vi v x = const ; 303L: Electric Fields (Ch.22) v y = ayt = − eE t; me x f = vi t ; yf = − 1 2 • The electrons are deflected in various directions by two sets of plates eE 2 t; me Example 6 303L: Electric Fields (Ch.22) 2 SUMMARY The Electric Field r rF E≡ e q0 ⇒ r r Fe = qE 303L: Electric Fields (Ch.22) 3 ...
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