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Transcript
Announcements: Tutorials Tutorials: Monday 6-8pm Ryan Best Tuesday 4:30-6:30pm Christine Carlisle Wednesday 4:30-6:30pm Christine Carlisle Thursday 6-8pm Ryan Best Tentatively Olin 103 Learning Assistance Center: [email protected] Has done group tutoring before for Phy 113 . 1 Announcements: Labs and Webassign Buy the lab manual Lab’s start next week. Sections A-C are virtually full, section D is nearly empty. Webassign 3 people didn’t do the reading quiz for today. Note, I often comment on reading quizzes. registration requires an access code online or bookstore 2 Recap When due?due? Suppose a plane flies 100 miles NW. Whenare arehomeworks reading quizzes A) A) MWF MWF7am 7am What is the displacement of the B) B) MWF MWF10pm 10pm plane? C) C) TR TR7am 7am D) A)70.7 x + 70.7 y D) FF10pm 10pm B) -70.7 x + 70.7 y C) 100 x D)100 y Vector Multiplication There are two ways (in 2 or 3D) to multiply vectors. Scalar product -> two vectors make a scalar A ●B =N Also called the dot product or the inner product Vector product -> two vectors make a vector AxB=C Also called the cross product, alternating product or the outer product Scalar Product Scalar product -> two vectors make a scalar A ●B =ABcos q A ●B =axbx+ayby+azbz Geometric Algebraic Vector Product Vector product -> two vectors make a vector AxB=C Geometric C has magnitude absinq. Direction perpendicular to the plane containing A and B. A x B = (aybz-byaz)i+(azbx-bzax)j+(aAlgebraic xby-bxay)k The right hand rule Force F velocity v Magnetic Field B F=q(v x B) Electricity and Magnetism •One of the four fundamental forces of nature •Responsible for the vast majority of what we observe around us •Probably best-understood and best-tested of the forces of nature Electromagnetic Interactions: •Electricity and Electronics •Magnetism •Chemistry •Biology • and even more Electrical Charges •Electric forces only affect objects with charge •Charge is measured in Coulombs (C). A Coulomb is a large unit of charge. 1 electron has -1.6 x 10-19 C of charge. •Charge comes in both positive and negative quantities •Charge is conserved – it can neither be created nor destroyed •Charge is usually denoted by the letter q. An object has a total charge of 5 mC. It is divided into two pieces, one of which has charge 8 mC and the other of which has charge A) 3 mC B) -3 mC C) 13 mC D) Such a division is impossible Matter and Charges •All matter is made of positive and negative charges (or neutral) •An object’s total charge is very close to zero •When an object becomes charged, a tiny fraction of its charged particles (usually electrons) are lost or gained •These particles (usually electrons) can flow through objects What do you think of when you hear the words conductor or insulator? Conductor A material that allows electrons or other charged particles to flow freely Insulator A material that resists the flow of electrons and other charged particles Elementary Charge •Charges exist in integer multiples of a fundamental charge unit called e •We will consider e to be a positive number (some sources treat it as negative) e = 1.602 10-19 C the magnitude of the charge on an electron. the charge on a proton When you write that an atom or molecule has a charge +1 , you mean +e. A partial charge means that a charge density can be modeled as having a charge at a location less than e Charge Densities Charge can be localized to discrete points (point charges), or it may be spread out over a volume, a surface or a line •Charge density units C/m3 •Surface charge density units C/m2 •Linear charge density units C/m A cube with side 1 cm has a charge density of = 1 C/m3. What is the charge of the cube? A) 1 C B) 0.01 C = 10 mC C) 10-4 C = 100 m C 1 cm D) 10-6C = 1 mC 12 Coulomb’s Law •Like charges repel, unlike charges attract •Force is directly along a line joining the two charges q1 ke q1q2 Fe rˆ 2 r q2 r q1q2 Fe rˆ 2 4 0 r 0 = 8.85410-12 C2/ (N●m2) •Permittivity of free space •An inverse square law, just like gravity •Can be attractive or repulsive – unlike gravity 13 •Constant is enormous compared to gravity Coulomb’s Law: Applied A Helium nucleus (charge +2e) is separated from one of its electrons (charge –e) by about 3.00 10-11m. What is the force the nucleus exerts on the electron? Is it attractive or repulsive? ke q1q2 9 Nm2/C2 k = 8.98810 Fe e 2 r -11m the force on the electron rHow = just 3.00 10 We calculated from the q1 =of3.204 10-19C does the acceleration the nucleus compare nucleus. does this q2 =compare -1.602 with 10-19the C force to that ofHow the electron? theacceleration nucleus from the nucleus electron?is larger A) on The of the A) on themN nucleus is twiceisassmaller big The acceleration of the Attractive nucleus FB)e=The - force 0.513 Force B) The force on the nucleus is half as big C) The accelerations are equal. C) The forces are equal in magnitude 14 Newton’s Laws and Kinematics Fnet ma Newton’s laws and all the kinematics you learned in 113 are still true! F12 F21 t' t' dx dv v ;a v adt vt0 ; x vdt x0 dt dt t0 t0 If a does not depend on time, then 1 2 v at v0 ; x at v 0 t x 0 2 15