Physics II: Electricity & Magnetism

Physics II:Electricity & Magnetism Section 21.11

Thursday (Day 16)

Warm-Up Thurs, Feb 12 • Complete Graphic Organizers for Sections 21-8 & 21-10. • Place your homework on my desk: • “Foundational Mathematics’ Skills of Physics” Packet (Page 18) • Web Assign 21.12 - 21.14 • For future assignments - check online at www.plutonium-239.com

Essential Question(s) • WHAT PRIOR FOUNDATIONAL MATHEMATICS’ SKILLS ARE NECESSARY IN PHYSICS II? • HOW DO WE DESCRIBE THE NATURE OF ELECTROSTATICS AND APPLY IT TO VARIOUS SITUATIONS? • How do we compare and contrast the basic properties of an insulator and a conductor? • How do we describe and apply the concept of electric field?

Static Electricity Electric Charge Positive / Negative Attraction / Repulsion Charging / Discharging Friction Induction Conduction Law of Conservation of Electric Charge Non-polar Molecules Polar Molecules Ion Ionic Compounds Force Derivative Integration (Integrals) Test Charge Electric Field Field Lines Electric Dipole Dipole Moment Vocabulary

Foundational Mathematics Skills in Physics Timeline WHAT PRIOR FOUNDATIONAL MATHEMATICS’ SKILLS ARE NECESSARY IN PHYSICS II?

Agenda • Review “Foundational Mathematics’ Skills of Physics” Packet (Page 18) with answer guide. • Discuss • Torque, factors that affect torque, r X F • Electric Dipoles • Electric Dipoles in an Electric Field • The electric field produced by a dipole • Calculations: Dipoles in an electric field

Section 21.11 • How do we compare and contrast the basic properties of an insulator and a conductor? • What are characteristics and classification(s) of electrically . . . • conductive atoms? • insulative atoms? • semi-conductive atoms? • conductive compounds? • insulative compounds? • semi-conductive compounds?

Section 21.11 • How do we describe and apply the concept of electric field? • How do we calculate the net force and torque on a collection of charges in an electric field? How do we calculate the net force and torque on a collection of charges in an electric field?

Torque To make an object start rotating, a force is needed; the position and direction of the force matter as well. The perpendicular distance from the axis of rotation to the line along which the force acts is called the lever arm. How do we calculate the net force and torque on a collection of charges in an electric field?

Torque A longer lever arm is very helpful in rotating objects. How do we calculate the net force and torque on a collection of charges in an electric field?

Torque Here, the lever arm for FA is the distance from the knob to the hinge; the lever arm for FD is zero; and the lever arm for FC is as shown. How do we calculate the net force and torque on a collection of charges in an electric field?

Torque • The torque is defined as: • = rF or • = r F

Torque,  • Torque is perpendicular to the direction of the rotation. • Right-hand rule - The direction of the positive torque is in the direction of increasing angle) • In general, if we define torque as  =r x F = r F sin  • Also, torque can be defined about any point using net =(ri x Fi) • where ri is the position vector of the ith particle and Fi is the net force on the ith particle. How do we calculate the net force and torque on a collection of charges in an electric field?

Bond Types (Revise) • Covalent: share electrons equally • Ionic Transfer electrons (each ion has full charge) • Polar covalent: share electrons unequally (both atoms that make up the bond have a slightly positive or negative charge - they do not have full charge)

Electronegativity Activity • I.e. similar to organic chemistry Section 1.10?

Electric Dipoles • The combination of two equal charges of opposite sign, +Q and -Q , separated by a distance l, is referred to as an electric dipole. The quantity Ql is called the dipole moment, p. The dipole moment points from the negative to the positive charge. Many molecules have a dipole moment and are referred to as polar molecules. • It is interesting to note that the value of the separated charges may be less than that of a single electron or proton but cannot be isolated. How do we calculate the net force and torque on a collection of charges in an electric field?

Electric Dipoles • Electric Dipoles: The combination of two equal charges of opposite sign, +Q and -Q, separated by a distance l. • The dipole moment, p: The quantity Ql. • The dipole moment points from the negative to the positive charge. • Many molecules have a dipole moment and are referred to as polar molecules. • It is interesting to note that the value of the separated charges may be less than that of a single electron or proton, but they cannot be isolated.

Relating Induced Electric Dipole to Dipole Moments

Dipole in an External Field A dipole, p = Ql, is placed in an electric field E. First, let us analyze the angle , for torque and about its bisector at point O. +q F± F± -q Note that the choice of the angle does not change our value for sin  point O will be used for all reference angles instead of the rxF angle to relate the direction of the dipole moment to the E-Field. How do we calculate the net force and torque on a collection of charges in an electric field?

Dipole in an External Field A dipole, p = Ql, is placed in an electric field E. Next, let us analyze the direction of the torque force to the change angle , Note: By definition, positive torque always increases the value of  (I.e. move the dipole in the counterclockwise direction). It is also important to note that the applied torque force will cause the angle  decrease (in the clockwise direction) instead of increase (counter-clockwise) about point O.   about point O is negative. How do we calculate the net force and torque on a collection of charges in an electric field?

Dipole in an External Field A dipole p = Ql is placed in an electric field E. How do we calculate the net force and torque on a collection of charges in an electric field?

Dipole in an External Field The effect of the torque is to try to turn the dipole so p is parallel to E. The work done on the dipole by the electric field to change the angle from  to  , is Because the direction of the torque is opposite to the direction of increasing , we write the torque as Then the dipole so p is parallel to E. The work done on the dipole by the electric field to change the angle from  to  , is How do we calculate the net force and torque on a collection of charges in an electric field?

Dipole in an External Field + Positive work done by the field decreases the potential energy, U, of the dipole in the field. If we choose U = 0 when p is perpendicular to E (that is choosing  = 90º so cos  = 0), and setting  =  then + – How do we calculate the net force and torque on a collection of charges in an electric field?

Dipole in an External Field Positive work done by the field decreases the potential energy, U, of the dipole in the field. If we choose U = 0 when p is perpendicular to E (that is choosing  = 90º so cos  = 0), and setting  =  then – + + How do we calculate the net force and torque on a collection of charges in an electric field?

Torque with respect to the Dipole’s Orientation How do we calculate the net force and torque on a collection of charges in an electric field?

Electric Field Produced by a Dipole To determine the electric field produced by a dipole in the absence of an external field along the midpoint or perpendicular bisector of the dipole. + – h h h r at r >> L How do we calculate the net force and torque on a collection of charges in an electric field?

Electric Field Produced by a Dipole It is interesting to note that at r >> l, the electric field decreases more rapidly for a dipole (1/r3) than for a single point charge (1/r2). This is due to the fact that at large distances the two opposite charges neutralize each other due to their close proximity At distances where r >> l, this 1/r3 dependence also applies for points that are not on the perpendicular bisector of the dipole. + – h h h r For a dipole at r >> l For a single point charge How do we calculate the net force and torque on a collection of charges in an electric field?

Table of Dipole Moment Values How do we calculate the net force and torque on a collection of charges in an electric field?

Dipoles in an Electric Field • The dipole moment of a water molecule is 6.1 x 10-30 C•m. A water molecule is placed in a uniform electric field with magnitude 2.0 x 105 N/C. • What is the magnitude of the maximum torque that electric field can exert on the molecule? • What is the potential energy when the torque is at its maximum? • What is the dipole moment, p1 and p2, for a single O-H bond (where 2 = 104.5°)? Note: Let How do we calculate the net force and torque on a collection of charges in an electric field?

Dipoles in an Electric Field • The dipole moment of a water molecule is 6.1 x 10-30 C•m. A water molecule is placed in a uniform electric field with magnitude 2.0 x 105 N/C. • In what position will the potential energy take on its greatest value? • Why is this different than the position where the torque is maximized? The potential energy will be maximized when cos  = –1, so  = 180°, which means p and E are antiparallel. The potential energy is maximized when the dipole moment is oriented so that it has to rotate through the largest angle, 180°, to reach equilibrium at  = 0°. The torque is maximized when the electric forces are perpendicular to p. How do we calculate the net force and torque on a collection of charges in an electric field?

Dipoles in an Electric Field • The carbonyl group (C=O) dipole. The distance between the carbon (+) and oxygen (–) atoms in the carbonyl group which occurs in many organic molecules is about 1.2 x 10-10 m and the dipole moment of this group is about 8.0 x 10-30 C•m. A formaldehyde molecule, CH2O, is placed in a uniform electric field with magnitude 2.0 x 105 N/C. • What the direction of the dipole moment, p? • What is the magnitude of the maximum torque that electric field can exert on the molecule? • What is the potential energy when the torque is at its maximum? How do we calculate the net force and torque on a collection of charges in an electric field?

Dipoles in an Electric Field • The carbonyl group (C=O) dipole. The distance between the carbon (+) and oxygen (–) atoms in the carbonyl group which occurs in many organic molecules is about 1.2 x 10-10 m and the dipole moment of this group is about 8.0 x 10-30 C•m. A formaldehyde molecule, CH2O, is placed in a uniform electric field with magnitude 2.0 x 105 N/C. • What is the partial charge (±) of the carbon (+) and oxygen (–) atoms in the carbonyl group? • (a) How much of the quantized charge of an electron/proton is the partial charge of the carbonyl group to? (b) What is this value in percent? How do we calculate the net force and torque on a collection of charges in an electric field?

Dipoles in an Electric Field • The carbonyl group (C=O) dipole. The distance between the carbon (+) and oxygen (–) atoms in the carbonyl group which occurs in many organic molecules is about 1.2 x 10-10 m and the dipole moment of this group is about 8.0 x 10-30 C•m. A formaldehyde molecule, CH2O, is placed in a uniform electric field with magnitude 2.0 x 105 N/C. • In what position will the potential energy take on its greatest value? • Why is this different than the position where the torque is maximized? The potential energy will be maximized when cos  = –1, so  = 180°, which means p and E are antiparallel. The potential energy is maximized when the dipole moment is oriented so that it has to rotate through the largest angle, 180°, to reach equilibrium at  = 0°. The torque is maximized when the electric forces are perpendicular to p. How do we calculate the net force and torque on a collection of charges in an electric field?

Summary • How does positive torque relate to the change in the angle? • HW (Place in your agenda): • “Foundational Mathematics’ Skills of Physics” Packet (Page 19) • Web Assign 21.15 • Future assignments: How do we calculate the net force and torque on a collection of charges in an electric field?

Supplementary Notes

Vector Cross Product • Known as the vector product or cross product • The cross product of two vectors A and B is defined as another vector C = A x B whose magnitude is C = |A x B| = AB sin  where  < 180º between A and B and whose direction is perpendicular to both A and B. • Right hand rules for cross products

Vector Cross Product • The cross product of two vectors • A = Axi + Ayj + Azk • B = Bxi + Byj + Bzk • Can be written as A x B = (AyBz-AzBy)i + (AzBx-AxBz)j + (AxBy-AyBx)k

Properties of Vector Cross Products • A x A = 0 • A x B = -B x A • A x (B + C) = (A x B) + (A x C) • .

Physics II: Electricity & Magnetism