Exam #1 Attention: Midterm test #1 will be given in Lecture class on Wednesday October 5 starting at noon. One hour long For students requiring extra time: Please contact the Learning Assistance Services Fill the form, let me sign it and arrange the time for your test If you have a conflict with a religious holiday – alternative time – Monday 10/3 – 3pm Sign up after class 11/15/2018 Lecture VI
Work to move a charge + + + - How much work has to be done by an external force to move a charge q=+1.5 mC from point a to point b? Work-energy principle + 30cm + 20cm 15cm 25cm + - Q1=10mC Q2=-20mC 11/15/2018 Lecture VI
Determine E from V Think ski slopes If V depends on one coordinate x E is directed along x from high V to low If V depends on x,y,z 11/15/2018 Lecture VI
E near metal sphere Find the largest charge Q that a conductive sphere radius r=1cm can hold. Air breakdown E=3x106V/m Near surface: E=V/r Larger spheres can hold higher voltage 11/15/2018 Lecture VI
Capacitance Physics 122 11/15/2018 Lecture VI
Concepts Primary concepts: Capacitor and capacitance Storing electric energy and charge Dielectrics 11/15/2018 Lecture VI
Laws Charge on a capacitance Capacitance formula Capacitance with dielectric Energy in a capacitance 11/15/2018 Lecture VI
Capacitance Two parallel plates are called a capacitor. When capacitor is connected to a battery plates will charge up. Note: net charge =0 C – coefficient, called capacitance, property of the capacitor. Capacitance is measured in Farad (F=C/V) 11/15/2018 Lecture VI
Electric field in a capacitor E=const E= V/d points from high potential to low When V is fixed (same battery), E depends only on the d. Potential High next to + plate Low – next to - plate 11/15/2018 Lecture VI
Capacitance Capacitance depends on the geometry of a capacitor e0 = 8.85. 10-12 C2/N m2- permittivity of free space A – area of plates (m2) Same sign charges want to “spread out” – to hold more charge need large area d – distance between plates (m) Opposite sign charges “hold” each other, attraction is stronger for shorter d A d 11/15/2018 Lecture VI
Dielectrics Put non-conductive material (dielectric) between plates Can hold more charge capacitance increases K(>1) – dielectric constant 11/15/2018 Lecture VI
Charging up a capacitor Find the work needed to charge a capacitor C to voltage V Take small charge dq and move it across the capacitor, which is at voltage V at this moment dW=Vdq 11/15/2018 Lecture VI
Energy storage Work to charge a capacitor= potential energy stored in the capacitor To use the right formula, watch what is kept constant V=const – if C connected to a battery Q=const - if C disconnected 11/15/2018 Lecture VI
Inserting dielectric Capacitor is connected to a battery, supplying voltage V. How will the energy stored in the capacitor change if we insert a dielectric (K=2)? CKC=2C – capacitance increases V stays const – same battery Q changes 11/15/2018 Lecture VI
Inserting dielectric Capacitor is charged to charge Q and disconnected from a battery. How will the energy stored in the capacitor change if we insert a dielectric (K=2)? CKC=2C – capacitance increases V can change Q stays const – charge conservation 11/15/2018 Lecture VI
Inserting dielectric Disconnected battery – Connected battery – energy decreases Dielectric will be “sucked in” Connected battery – energy increases Dielectric will be “pushed out” 11/15/2018 Lecture VI
Test problem Between two very large oppositely charged parallel plates at which of the three locations A, B and C electric potential is the greatest? A A B B C C D Equal at all three locations. 11/15/2018 Lecture VI
Capacitor connections Three capacitors connected to a battery in Parallel: Same voltage at capacitors C1, C2, C3 V1=V2=V3=V Different charges: Q1=C1V Q2=C2V Q3=C3V Total charge stored on three capacitors: Q=Q1+Q2+Q3=V(C1+C2+C3) Ceq=C1+C2+C3 No DC current through capacitor, Just store charge. 11/15/2018 Lecture VI
Capacitor connections Three capacitors connected in series Same charge on each capacitor (QA=0 -Q1+Q2=0) Q1=Q2=Q3 Different voltages V=V1+V2+V3 11/15/2018 Lecture VI