Electric Field q1 q2 r 1,2 1,2 1,2 Question: Why q1 can feel q2 without direct contact? just as air around us, there’re something around a charge, i.e. electric field (photons) that transfer the force. During last class, we talked about How to charge an object via contact (e.g. rubbing) and induction How to quantitively describe the interaction between charges via coulomb’s law Today we will learn a new concept: electric field that will be frequently used in this class.

Electric Field Define electric field, which is independent of the test charge, q, and depends only on position in space: q F Q Electric Field due to a Point Charge Q Field will always accompany a charge Q and is independent of any other charges. when a second charge q present, q will feel the force because of its interaction with the force. Source charge Q and test charge q. The field of the Q is defined as E=F/q, i.e. independent of the test charge. Equal to Force per unit test charge. Talk about the direction of the E field for +q and –q. Direction of Electric Field point away from positive charges Point to negative charges.

Electric Field With this concept, we can “map” the electric field anywhere in space produced by any arbitrary charge: a Vector field 77 82 83 68 55 66 75 80 90 91 71 72 84 73 57 88 92 56 64

Electric Field due to Multiple Point Charges The force on a test charge is then given by F1 + q0 F2 so the electric field is, by definition, given by F3 Principle of Superposition!

Example: Two charges of the same magnitude Both charges > 0 x One is > 0, the other < 0 -q q electric dipole of dipole moment: if |qL|>|qR| if |qR|>|qL|

A visualization tool to illustrate the geometry of an electric field. Electric Field Lines A visualization tool to illustrate the geometry of an electric field. Electric field lines originate from positive charges and terminates at negative charges. The direction of the electric field at any location is tangential to the field line there. The magnitude of the electric field at any location is proportional to the density of the lines there. (or at infinity) # lines/area ~ 1/r2 ~ |E|

Electric field lines of two charges of equal magnitude dipole Field lines do NOT cross They do NOT come out of nowhere or vanish into a point. Far from the charges, electric field lines resemble those of a point charge.

Electric field lines of two charges Far from charges, the field lines are as if they are due to a point charge of +2q-q=+q # lines proportional to the magnitude of charge Show the field from the parallel plate capacitor since it will be used when talking about slide #11 http://www.its.caltech.edu/~phys1/java/phys1/EField/EField.html http://www.falstad.com/vector3de/

Warm-up quiz What is the direction of the electric field at the center of the two point charges? (Take Q > 0.) toward the lower right toward the upper left upward to the right none of the above -Q Q

Point Charge in an Electric Field Electrostatic force on the charge q due to E: E acting on the charge is produced by the other charges (external field). Dimension of E = [force]/[charge] and its SI units = N/C Work done by E on q in moving the charge: F is parallel to E if the charge is positive and anti-parallel if the charge is negative The charge is not affected by its own electric field. Conservative force like the gravity. W is path( )-independent => Conservative force

Dynamics of a Charge in Electric Field For -Q<0 in uniform E downward: -Q Oscilloscope Ink-Jet Printing Neglect the gravitational force since it’s negligible compared with the electric force. Determine the relative among Y, X, E, m and Q. One can determined Q from X, Y, E and m=>oil drop experiment to measure the charge on electron. One can control Y via control other 3 quantities=>Oscilloscope and Ink-Jet Printing. Oil drop experiment http://canu.ucalgary.ca/map/content/force/elcrmagn/simulate/electric_single_particle/applet.html

Electric Field due to an Electric Dipole At point P on z-axis: Use principle of superposition: Get field from +q and –q, respectively and add then together. Where is the (magnitude of) dipole moment.

Dipole Field Anisotropy z  y At point P on y-axis: Dipole Field at General Point P: where is the unit vector from the center of dipole to the observation point P.

General definition of dipole moments exists: Electric Dipoles Typical dipole consists of positive and negative charges slightly displaced. General definition of dipole moments exists: Water molecule can be thought of as consisting of 2 standard dipoles at an angle to each other. Net neutral molecules can have electrical dipole moments Permanent dipole moment (polar) vs. induced dipole moment Permanent: like the water molecules Induced: like the paper bit picked up by the charged glass rod from last class.

Dipole in uniform electric fields No net force. The electrostatic forces on the constituent point charges are of the same magnitude but along opposite directions. So, there is no net force on the dipole and thus its center of mass should not accelerate. Net torque! There is clearly a net torque acting on the dipole with respect to its center of mass, since the forces are not aligned. Clockwise about the center of mass http://qbx6.ltu.edu/s_schneider/physlets/main/dipole_torque.shtml

Torque on the Dipole x q F CM The magnitude of the torque: The torque points into the screen.

Physics 241 – Sample Quiz A – January 9, 2008 Four point charges are arranged at the corners of a square as shown. What is the direction of the electric field at the center of the square? (Take Q > 0.) toward the lower right toward the upper left upward to the right none of the above -Q - Q Q Q

Physics 241 – Sample Quiz B – January 9, 2008 Four point charges are arranged at the corners of a square as shown. What is the direction of the electric field at the center of the square? (Take Q > 0.) toward the lower right toward the upper left upward to the right none of the above Q - Q Q Q

Physics 241 – Sample Quiz C – January 9, 2008 Three point charges are arranged at three of the corners of a square as shown. What is the direction of the electric field at the center of the square? (Take Q > 0.) toward the lower right toward the upper left upward to the right none of the above Q Q Q