Physics 2102 Jonathan Dowling Physics 2102 Lecture 03 FRI 16 JAN Electric Fields I January 14 09 Version 1 14 09 Charles Augustin de Coulomb 1736 1806 What Are We Going to Learn A Road Map Electric charge Electric force on other electric charges Electric field and electric potential Moving electric charges current Electronic circuit components batteries resistors capacitors Electric currents Magnetic field Magnetic force on moving charges Time varying magnetic field Electric Field More circuit components inductors Electromagnetic waves light waves Geometrical Optics light rays Physical optics light waves Coulomb s Law q1 F12 F21 r12 k q1 q2 F12 2 r12 q2 For Charges in a Vacuum 2 N m 9 8 99 10 k C2 Often we write k as k 1 4 0 with 0 8 85 10 12 2 C N m2 E Field is E Force Divided by E Charge F E q Definition of Electric Field k q1 q2 F12 2 r12 k q2 E12 2 r12 E Force on Charge E Field at Point Units F N Newton E q1 F12 P1 P2 E12 P1 q2 q2 P2 N C Newton Coulomb Electric Fields Electric field E at some point in space is defined as the force experienced by an imaginary point charge of 1 C divided by 1 C Electric Field of a Point Charge q E Since E is the force per unit charge 1C R it is measured in units of N C Note that E is a VECTOR We measure the electric field using very small test charges and dividing the measured force by the magnitude of the charge k q E 2 R Superposition of F and E Question How do we figure out the force or field due to several point charges Answer consider one charge at a time calculate the field a vector produced by each charge and then add all the vectors superposition Useful to look out for SYMMETRY to simplify calculations Example Total electric field 2q q 4 charges are placed at the corners of a square as shown What is the direction of the electric field at the center of the square q y 2q a Field is ZERO b Along y c Along x x Electric Field Lines Field lines useful way to visualize electric field E Field lines start at a positive charge end at negative charge E at any point in space is tangential to field line Field lines are closer where E is stronger Example a negative point charge note spherical symmetry Direction of Electric Field Lines E Field Vectors Point Away from Positive Charge Field Source E Field Vectors Point Towards Negative Charge Field Sink Electric Field of a Dipole Electric dipole two point charges q and q separated by a distance d Common arrangement in Nature molecules antennae Note axial or cylindrical symmetry Define dipole moment vector p from q to q with magnitude qd Cancer Cisplatin and electric dipoles http chemcases com cisplat cisplat01 htm Electric Field On Axis of Dipole q a q P x Superposition E E E E kq a x 2 2 1 1 E kq 2 2 a a x x 2 2 E kq kq a x 2 2 xa 2 2 2 a x 4 2 Electric Field On Axis of Dipole E kq 2 xa 2 2 2 a x 4 p qa dipole moment a VECTOR 2kpx 2 2 2 a x 4 What if x a i e very far away 2kpx 2kp E 4 3 x x E p r 3 E p r3 is actually true for ANY point far from a dipole not just on axis Force on a Charge in Electric Field Definition of Electric Field Force on Charge Due to Electric Field F E q F qE Force on a Charge in Electric Field E Positive Charge Force in Same Direction as EField E Negative Charge Force in Opposite Direction as EField Electric Dipole in a Uniform Field Net force on dipole 0 center of mass stays where it is Net TORQUE INTO page Dipole rotates to line up in direction of E 2 qE d 2 sin qd E sin p E sin p x E The dipole tends to align itself with the field lines What happens if the field is NOT UNIFORM Distance Between Charges d
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