1 Lecture 4 Today in Phys 1302 • Electrostatics review • Cottrell precipitator Announcement: • Phys 1302W.500 Quiz 1: Chapters 21, 22, 23 Monday, Feb 9: in discussion sections -one long problem, 25 points Wednesday, Feb 11: 50 minute in class (150 Phys) -two long problems, 25 points each -five multiple choice problems At least work these problems: 21: 10, 43, 44, 55 63, 67 22: 6, 8, 22, 45, 66, 70 23: 25, 33, 35, 42, 47, 51, 56 Announcement: • Phys 1302W.500 Clicker Questions Tuesday, Feb 2: these PRS “clicker” questions will count toward your grade starting today. 2 Lecture 4 Cottrell • http://en.wikipedia.org/wiki/Electrostatic_precipitator • http://www.rescorp.org/ Cottrell (on right) photograph taken in 1916, and Walter A. Schmidt, president of Western Precipitation Company. Review: problem 21.67 problem 22.22 Which figure below best shows 1. 2. 3. 4. 5. 3 Lecture 4 Which figure best shows 1. 2. 3. 4. 5. What are the x- and y-components Cx and Cy of vector 1. Cx= –3 cm, Cy = 1 cm 2. Cx= –4 cm, Cy = 2 cm 3. Cx= –2 cm, Cy = 1 cm 4. Cx= –3 cm, Cy = –1 cm 5. Cx= 1 cm, Cy = –1 cm x x σ x x σ/2σ/2 (a) Write down the electric field E at the point x. (b) Would the field change if the slab were moved further to the left? (c) Would the field change if the thickness of the slab were increased? (d) Would the field change if the slab were replaced by two slabs, each carrying charge density s/2? E = σ/2εo No No No 4 Lecture 4 x x σ x x σ/2σ/2 how to deal with conductors? Suppose that the slab described above were made of metal instead of non- conducting material … what would change? (f) Would the field outside the slab (e.g. at the point x) change? (g) Would the field inside the slab change? (h) Would the distribution of charge within the slab change? How so? no, σ is still the same outside yes, field inside is zero yes, charge is all on surface of the plates Two non-conducting slabs of infinite area are given a charge-per-unit area of σa = -4 C/m2 and σb =+1.5 C/m2 respectively. A third slab, made of metal, is placed between the first two plates. x σm σbσa y metal non-conductingnon-conducting σa = -4 C/m2 σb = +1.5 C/m2 σm = 0 BA C The charge density sm on the metal slab is 0 (i.e. the slab is uncharged). x σm σbσa y metal non-conductingnon-conducting σa = -4 C/m2 σb = +1.5 C/m2 σm = 0 BA C (a) Find the magnitude and direction of the electric field at the points A, B, and C. EA = EB = (-5.5 C/m2)/2εo EC = (-2.5 C/ m2)/2εo All in negative x-direction. 5 Lecture 4 x σm σbσa y metal non-conductingnon-conducting σa = -4 C/m2 σb = +1.5 C/m2 σm = 0 BA C (b) Now let’s think physically about the metal slab. The defining property of a conductor is that the charges within are free to move, and they will do so in response to an electric field. As a result, surface charges σL and σR will accumulate on the left- and right-hand surfaces of the slab. What are the signs of these surface charges? σL – positive σR - negative x σm σbσa y metal non-conductingnon-conducting σa = -4 C/m2 σb = +1.5 C/m2 σm = 0 BA C (c) Go ahead and use Gauss’ Law plus your answers to question (a) to calculate the surface charges σL and σR induced on the metal slab. σL = 2.75 C/m2 σR = -2.75 C/m2 A total charge Q is uniformly distributed over the length L of a line charge distribution. The charge density λ is given by L Q dxLQ Q L Q 1. 2. 3. 4. 5. None of the above. L Q 6 Lecture 4 A total charge Q is uniformly distributed over the length L of a line charge distribution. The total charge inside a short element dx is given by 1. 2. 3. 4. 5. None of the above. g115 g120 g139g159g115g120 g120 g115 g120g139g159 L Q dx A total charge Q is uniformly distributed over the length L of a line charge distribution. The Y component of electric field at point P created by a short element dx is given by: r a r dxLQK × 2 r x r dxLQK × 2 x a r dxLQK × 2 axr dxLQK × 2 1. 4. 2. 3. Q r a x P L dx Ct1 A positive charge is fixed at the center inside a fixed spherical neutral conducting shell. Which of the following represents the charge distribution on the inner and outer walls of the shell? 7 Lecture 4 ct2 A positive charge is kept fixed off-center inside a fixed spherical neutral conducting shell. Which of the following represents the charge distribution on the inner and outer walls of the shell? Shielding Demonstration • We will demonstrate shielding in two ways • We will place Styrofoam peanuts in a container on a Van de Graaff generator – In a metal cup – In a plastic cup – Note that the shielding effect does not require a solid conductor • A wire mesh will also work, as long as you don’t get too close to the open areas Lightning Strikes a Car The crash-test dummy is safe, but the right front tire didn’t make it … High Voltage Laboratory, Technical University Berlin, Germany 8 Lecture 4 ct3 A positive charge Q is kept fixed at the center of a spherical neutral conducting shell. A negative charge –Q is brought near the outside of the sphere. Which of the following represents the charge distributions? Admin Microsoft PowerPoint - 1302W.500_lecture_5