COULOMB FORCE Charge q1 “Test Charge” q2 r 1,2 1,2 1,2 “Is action at a distance possible?” Question: How can q1 sense q2 without direct contact? NO! just as air around us, there’re some medium around a charge, the electric field that transfers the force.

READING QUIZ 1 HOW DOES THE MAGNITUDE OF THE ELECTRIC FIELD E FROM A POINT CHARGE Q DEPEND ON THE MAGNITUDE OF Q AND THE DISTANCE R TO THE FIELD POINT? E = k Q Q / R2 E = k Q / R E = k Q / R2 E = k Q Q / R E = k Q / R3

Electric Field Define electric field, which is independent of the test charge, q2 , and depends only on position in space: Electric Field due to a Point Charge Q

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 A Vector field With this concept, we can “map” the electric field anywhere in space A Vector field 77 82 83 68 55 66 75 80 90 91 71 72 84 73 57 88 92 56 64

Demonstration Vandegraaff Generator

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.

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

Electric field lines of two unequal 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 http://www.its.caltech.edu/~phys1/java/phys1/EField/EField.html http://www.falstad.com/vector3de/

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

( Sum symbol Σ ) E = F/qO Σ Fx = 3.97 x 10-7 N Σ Fy = - 2.77 x 10-7 N F2 = Fx2 + Fy2 = (4.84 x 10-7 N)2 Tan Θ = Fy /Fx = - 34.9 O

Warm-up quiz 2 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 external 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. W is path( )-independent => Conservative force

Demonstration Dynamics of a charged Mass in an Electric field

Dynamics of a Charged Mass in Electric Field For -Q<0 in uniform E downward: -Q Oscilloscope Ink-Jet Printing vy = at = qE/m t vx >>0 Oil drop experiment http://canu.ucalgary.ca/map/content/force/elcrmagn/simulate/electric_single_particle/applet.html

The Electric Dipole Along the + z-axis Where p=qd is the magnitude of the dipole moment. The electric dipole is a vector in the direction from –q to +q. Let d 0 keep qd constant.This a point dipole

Dipole in a uniform external electric field 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.

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

Physics 241 – 10:30 Quiz 3 – January 14, 2010 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 – 11:30 Quiz 3 – January 14, 2010 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