Electric dipole, systems of charges Physics 122 9/22/2018 Lecture III

Workshops Due to low interest – 4 people and very limited resources I have to cancel one of the workshops: Fridays, 4-6 pm B&L 108A  Please let me know alternative times I’ll switch you to other workshops 9/22/2018 Lecture III

I am running Rochester marathon This Saturday, September 17, 8:00 am http://www.rochestermarathon.com/race.htm Starts and ends at Frontier field Goes along East and returns on Park Ave Lots of coffee shops and sit back, relax and watch people suffer 9/22/2018 Lecture III

Concepts Primary concepts: Secondary concepts: Electric field Electric dipole 9/22/2018 Lecture III

Laws Dipole field Dipole in electric field: energy and torque Superposition principle for a continuous distribution of charge 9/22/2018 Lecture III

Skills Calculate electric field of a system of charges 9/22/2018 Lecture III

Electric field + + F – force between two charges(N) Q – electric charge (C= Coulomb) E – electric field created at point 1 by charge 2 Charge 2 has changed the property of space at point 1 Charge 1 is experiencing this change + + 1 2 9/22/2018 Lecture III

Superposition of fields Principle of superposition: Net field created by a system of charges is a vector sum of fields created by individual charges: Positive test charge + + - 1 2 9/22/2018 Lecture III

Electric dipole -Q +Q l Two opposite charges of equal value Q separated by distance l Define dipole moment: A vector directed from negative charge to positive. Example – water molecule p1 H+ --O p H+ p2 9/22/2018 Lecture III

Electric Dipole Field Lines y Lines leave positive charge and return to negative charge What can we observe about E? Ex(x,0) = 0 Ex(0,y) = 0 x Field largest in space between two charges We derived: ... for r >> L, Demo Eb-1 (place on overhead, charge w/ Whimshurst) at the start. Note where there is symmetry 9/22/2018 Lecture III

Torque Force makes objects move  torque makes objects rotate 9/22/2018 Lecture III

How to add torques? + - You have to think… If the force acts to rotate the system counterclockwise – torque and angular acceleration are positive clockwise – torque and angular acceleration are negative Only relative sign matters + - 9/22/2018 Lecture III

How to add torques? + - Axis of rotation Axis of rotation 9/22/2018 Lecture III

How to add torques? - + Axis of rotation Axis of rotation 9/22/2018 Lecture III

Electric dipole Dipole in uniform E Net force F=F+-F-=0 Net torque 9/22/2018 Lecture III

Electric dipole Dipole in uniform E Energy - ? Work done by the field 9/22/2018 Lecture III

Energy of dipole in electric field -Q +Q -Q +Q -Q +Q Lowest energy state – dipole parallel to the field In electric field dipoles line up with the field 9/22/2018 Lecture III

Dipole in electric field -Q +Q In electric field dipoles line up with the field Dipole internal field anti-parallel in external field Net field is reduced 9/22/2018 Lecture III

Test question E - + If this region is filled with pure water (an excellent insulator), does the electric field… Increase? Decrease? Remain the same E - + The positive charge is shielded by the negative charges of the aligned dipoles (and vice versa). 9/22/2018 Lecture III

The Electric Field of a system of charges Bunch of Charges Charge Distribution + - + + + + + + + + + + + E=F/q. Superposition gives the sum (or integral!) 9/22/2018 Lecture III

Vectors by components r dq Charge Distribution r dq + E=F/q. Superposition gives the sum (or integral!) r, q are different for different charges and depend on your definition of the coordinate system, So choose it wisely 9/22/2018 Lecture III

Symmetry and coordinate systems Coordinate systems are there to help you You have a choice of System type Cartesian Cylindrical Spherical Origin (0,0), Direction of axis A good choice (respecting the symmetry of the system) can help to simplify the calculations 9/22/2018 Lecture III

Ring of charge A thing ring of radius a holds a total charge Q. Determine the electric field on its axis, a distance x from its center. a x q 9/22/2018 Lecture III

Charged disk Disk of radius R, uniformly charged with Q, determine E on the axis, a distance z above the center. Define charge density s =Q/pr2 Reuse previous results – divide disk into rings radius r, integrate over r from 0 to R. z 9/22/2018 Lecture III

Two parallel plates + - Infinite plates One positive, one negative, Same charge density s + - 9/22/2018 Lecture III

Long line of charge Determine the magnitude of the electric field at a distance x from a very long wire of uniformly distributed charge with linear charge density l (C/m). dq=ldy y q x 9/22/2018 Lecture III