# Phys 102 - Lecture 2 - University Of Illinois Phys 102 Lecture 2 Coulombs Law & Electric Dipoles 1 Today we will... Get practice using Coulombs law & vector addition Learn about electric dipoles Apply these concepts! Molecular interactions Polar vs. nonpolar molecules Hydrophilic vs. hydrophobic Permanent vs. induced dipole Chemistry! Phys. 102, Lecture 2, Slide 2 Recall: Coulombs Law Force between charges q1 and q2 separated a distance r: t ni g a M

e ud F12 F21 Force on q1 due to q2 o cti e r Di k q1 q2 2 r 1 q1 q2 2 40 r Coulomb constant

k 9 109 N m 2 C 2 Permittivity of free space 0 8.85 10 12 C 2 N m 2 n Opposite charges attract, like charges repel F12 F21 Phys. 102, Lecture 2, Slide 3 Superposition principle Total force on charge due to other charges = sum of individual forces Ftot F Ex: what is the force on q1 due to q2, q3, and q4? F13

q2 F12 q1 F12 F1,tot F14 F1,tot F14 q4

q3 F1,tot F12 F13 F14 F13 Order does not matter! Phys. 102, Lecture 2, Slide 4 Calculation: four charges Calculate the total force on charge q1 = +2 C C due to charges q2 = +7 C C, q3 = 3.5 C C Fundamental concept: Superposition F1tot F12 F13

q1 Approach: 4m q2 3m 3m Draw forces Calculate magnitudes of forces Add vectors Decompose into x-, y-components Add like components q3 May need geometry, trigonometry Phys. 102, Lecture 2, Slide 5

ACT: four charges Which vector best represents the total force on charge q1 = +2 C C due to charges q2 = +7 C C and q3 = 3.5 C C? A. q1 B. C. D. q2 q3 E. Phys. 102, Lecture 2, Slide 6 Calculation: four charges Calculate the total force on charge q1 = +2 C C due to charges q2 = +7 C C and q3 = 3.5 C C Calculate magnitudes of forces

q1 4m q2 3m 3m q3 Phys. 102, Lecture 2, Slide 7 ACT: components What is the x-component of F12 , F12,x? A. 3/4 F12 B. 3/5 F12 C. 4/5 F12

y x Decompose vectors into components q1 4m q2 3m 3m q3 Phys. 102, Lecture 2, Slide 8 ACT: components What is the y-component of F13 , F13,y? A. 3/4 F13

B. 3/5 F13 C. 4/5 F13 y x Decompose vectors into components q1 4m q2 3m 3m q3 Phys. 102, Lecture 2, Slide 9 Calculation: four charges Calculate the total force on charge q1 = +2 C C due to charges

q2 = +7 C C and q3 = 3.5 C C Add like components q1 4m q2 3m 3m q4 Phys. 102, Lecture 2, Slide 10 Calculation: four charges Calculate the total force on charge q1 = +2 C C due to charges q2 = +7 C C and q3 = 3.5 C C Magnitude of total force

Direction of total force q1 4m q2 3m 3m q3 Phys. 102, Lecture 2, Slide 11 ACT: CheckPoint 1.1 Consider three charges on a circular ring, q1 = +2q, q2 = q3 = +q. A charge +Q is placed at the center of the circle. 1 y

2q What is the x-component of the total force on Q? x A. Fx > 0 Q B. Fx = 0 C. Fx < 0 2 q 3 q Phys. 102, Lecture 2, Slide 12

ACT: CheckPoint 1.2 Consider three charges on a circular ring, q1 = +2q, q2 = q3 = +q. A charge +Q is placed at the center of the circle. 1 y 2q What is the y-component of the total force on Q? x A. Fy > 0 Q B. Fy = 0 C. Fy < 0 2 q

3 q Phys. 102, Lecture 2, Slide 13 Electric dipole & dipole moment A positive and negative charge of equal magnitude q separated by a (usually small) distance d +q d q = +q q = p

Dipole moment is measure of separated + and charges a M itu n g de p qd n tio c re Di From to + charge (by convention) Note: opposite from Lewis notation (Chemistry) definition What are examples of electric dipoles?

Phys. 102, Lecture 2, Slide 14 Molecular dipole Electrons are not shared equally between chemically bonded atoms Charge imbalance creates a bond dipole Ex: HF (hydrofluoric acid) Ex: H20 (water) Slightly negative Slightly positive 2- + p + p

+ Polar ptot > 0 Ex: CO2 (carbon dioxide) 2+ - - p 0 Nonpolar ptot = 0 Phys. 102, Lecture 2, Slide 15 ACT: CheckPoint 2.1 An electric dipole is placed near a large positive charge +Q. In what direction is the net force on the dipole? A. Left

+Q B. Zero C. Right q +q Phys. 102, Lecture 2, Slide 16 ACT: Dipole & 2 charges Consider an electric dipole placed an equal distance from a +Q and a Q charge. Does the dipole move? +q +Q q A. Yes Q B. No

Phys. 102, Lecture 2, Slide 17 Ion-dipole interactions Polar molecules are attracted to ions Dipole moment aligns away from + charge, toward charge Ex: ions in water & solubility Hydration shell Ionic compounds (ex: salts) dissolve in water Phys. 102, Lecture 2, Slide 18 Dipole-dipole interactions Polar molecules interact together Dipole moments align end-to-end + to Like magnets! Ex: hydrogen bond is a dipole-dipole interaction between water molecules Hydrogen bond Structure of ice Snowflake

Phys. 102, Lecture 2, Slide 19 Hydrophilic vs. hydrophobic Polar molecules interact with charged & polar molecules Ex: charged & polar molecules attract water, nonpolar molecules do not Hydrophilic Hydrophobic attract water repel water Hydrophilic Nonpolar inside Nonpolar Polar outside Polar coiled coil Hydrophobic

Oil and water Cell membranes Protein structure Phys. 102, Lecture 2, Slide 20 ACT: Charge & conductor An uncharged conducting sphere is placed next to a fixed + charge. What happens when the uncharged sphere is released? + DEMO A. Nothing B. Attracted to + sphere C. Repelled from + sphere Phys. 102, Lecture 2, Slide 21 Molecular interactions Interactions between molecules are understood in terms of charges and electric dipoles interacting by Coulombs law Ion-dipole

Dipole-dipole Dipole-induced dipole Induced dipoleinduced dipole? Ion-induced dipole Yes! Two nonpolar molecules can induce dipoles in each other and interact! London dispersion or van der Waals force Phys. 102, Lecture 2, Slide 22 Summary of todays lecture Coulombs law Superposition principle Ftot F Electric dipole & dipole moment Permanent vs. induced dipole Phys. 102, Lecture 2, Slide 23