AljalalPhys 102 142 Ch 22 page 1 Chapter

Aljalal-Phys 102 -142 --Ch 22 -page 1 Chapter 22 Electric Fields 22 -1 The Electric Field 22 -2 The Electric Field Due to a Point Charge 22 -3 The Electric Field Due to an Electric Dipole 22 -4 The Electric Field Due to a Line of Charge 22 -6 A Point Charge in an Electric Field 22 -7 A Dipole in an Electric Field Objective

Aljalal-Phys 102 -142 --Ch 22 -page 2 22 -1 The Electric Field of charged particles Charged particle q 1 sets up an electric field in all space. q 1 q 2 How does the point charge q 2 know about the presence of point charge q 1?

Aljalal-Phys 102 -142 --Ch 22 -page 3 22 -1 The Electric Field Definition To feel the electric field of a charged particle q 1 at a point P, we bring a positive charged particle q 0 at point P and measure the force F 01 on q 0 from q 1. P q 1 We call q 0 a test charge. q 0 We will define the electric field of charged particle q 1 at point P as

22 -1 The Electric Field Electric field from more than one charged particle q 2 P Aljalal-Phys 102 -142 --Ch 22 -page 4 The electric field from the charged particles q 1, q 2, q 3 at point P is q 1 q 3 q 0 At each point in space, you can find the electric field by the same method. q 0 is a positive test charge

Aljalal-Phys 102 -142 --Ch 22 -page 5 22 -1 The Electric Field Lines Representing electric field direction We use electric field lines to help us representing the electric field lines At any point, the tangent of the electric field lines gives the direction of the electric field.

22 -1 The Electric Field Lines Representing electric field strength Aljalal-Phys 102 -142 --Ch 22 -page 6 We use electric field lines to help us representing the electric field. Electric field lines Strong electric field Imaginary unit area Weak electric field Number of lines per unit area in a plane perpendicular to the electric field lines is proportional the magnitude of the electric field.

22 -1 The Electric Field Lines Electric field lines of a positive point charge q 0 Strong electric field Weak electric field q 0 is a positive test charge Aljalal-Phys 102 -142 --Ch 22 -page 7

Aljalal-Phys 102 -142 --Ch 22 -page 8 22 -1 The Electric Field Lines Electric field lines direction q 0 Electric field lines extend away from positive charge and toward negative charge.

Aljalal-Phys 102 -142 --Ch 22 -page 9 22 -1 The Electric Field Lines Electric field lines from a positive and a negative point charges q 0 Electric field lines extend away from positive charge and toward negative charge.

Aljalal-Phys 102 -142 --Ch 22 -page 10 22 -1 The Electric Field Lines Electric field lines from two equal and opposite point charges q 0 Electric field lines extend away from positive charge and toward negative charge.

Aljalal-Phys 102 -142 --Ch 22 -page 11 22 -1 The Electric Field Lines Electric field lines from a sphere of uniform negative charge q 0

Aljalal-Phys 102 -142 --Ch 22 -page 12 22 -1 The Electric Field Lines Electric field lines from a very large nonconducting sheet Side view

22 -2 The Electric Field Due to a Point Charge Formula P q For a point charge q 0 Aljalal-Phys 102 -142 --Ch 22 -page 13

22 -2 The Electric Field Due to a Point Charge Superposition principle q 2 q 1 Aljalal-Phys 102 -142 --Ch 22 -page 14 q 3 P Superposition principle

Aljalal-Phys 102 -142 --Ch 22 -page 15 22 -2 The Electric Field Due to a Point Charge Checkpoint 1 What is the direction of the electric field due to the electron at (a) point S (b) point R What is the direction of the net electric field at (c) point S (d) point R p -e S R Solution p -e S R

Aljalal-Phys 102 -142 --Ch 22 -page 16 22 -2 The Electric Field Due to a Point Charge Example 2 y What net electric field is produced at the origin? Solution y q 1 = +2 Q d 300 q 3 = - 4 Q d 300 x d 300 q 2 = - 2 Q x y Same magnitude 300 The electric field produced at the origin x has a magnitude of It points along the positive x-axis.

Review q q For a point charge P P Charge Unit vector Electric field due to a point charge q Use electric field lines to represent the electric field. At any point, the tangent of the electric field lines gives the direction of the electric field. Number of lines per unit area in a plane perpendicular to the electric field lines is proportional the magnitude of the electric field.

Aljalal-Phys 102 -142 --Ch 22 -page 18 22 -4 The Electric Field Due to an Electric Dipole Description Electric Dipole is two charges, which are equal in magnitude but of opposite sign and separated by a small distance d. +q d -q Dipole moment has a magnitude of p = q d and points towards the positive charge along the line joining the two charges

22 -3 The Electric Field Due to an Electric Dipole examples Aljalal-Phys 102 -142 --Ch 22 -page 19 Water molecule, H 2 O, is an electric dipole. The oxygen atom attracts the electrons of the hydrogen atoms. H H O More positive side More negative side Hydrogen chloride molecule, HCl, is an electric dipole. H The chlorine atom attracts the electrons of the hydrogen atom. Cl More positive side More negative side

22 -3 The Electric Field Due to an Electric Dipole Formula The electric field on the dipole axis at a distance that is large compared with The electric dipole moment the dipole dimensions of the dipole has a magnitude of p = q d and points from the negative to the positive end of the dipole Aljalal-Phys 102 -142 --Ch 22 -page 20 z Dipole axis +q d Distance from the dipole z >> d -q Origin at the Dipole midpoint

22 -3 The Electric Field Due to an Electric Dipole Comparison between a point charge an a dipole z Aljalal-Phys 102 -142 --Ch 22 -page 21 z +q +q -q If you double the distance from a single point charge, the electric field drops by a factor of 4. If you double the distance from a dipole, the electric field drops by a factor of 8. The reason for the rapid decrease in the electric field for a dipole is that the electric fields of the opposite charges almost cancel each other.

22 -3 The Electric Field Due to an Electric Dipole Derivation Show that on the dipole axis and for d << z Aljalal-Phys 102 -142 --Ch 22 -page 22 z z +q d -q For d << z

22 -4 The Electric Field Due to a Line of Charge Along a line of charge - 1 Find the electric field at point P y Optional for phys 102 -142 Aljalal-Phys 102 -142 --Ch 22 -page 23 A Line of charge of total charge – q, which is uniformly distributed along its length P L dx a small segment of length dx and charge dq x

22 -4 The Electric Field Due to a Line of Charge Along a line of charge - 2 Optional for phys 102 -142 Aljalal-Phys 102 -142 --Ch 22 -page 24 What is the electric field for a >> L ? We can write the electric field as For a >> L, the electric field is similar to that from a point charge.

Optional for 22 -5 The Electric Field Due to a Line of Charge On the perpendicular bisector of a line of charge - 1 Aljalal-Phys 102 -142 --Ch 22 -page 25 phys 102 -142 Find the magnitude of the electric field at point P located on the perpendicular bisector of the rod. P y a uniformly charged rod of charge q L

Optional for 22 -5 The Electric Field Due to a Line of Charge On the perpendicular bisector of a line of charge - 2 Aljalal-Phys 102 -142 --Ch 22 -page 26 phys 102 -142 q q small segment of length dx and charge dq y dx L dx x From symmetry, components along x-axis cancel each others. We need only to consider components along y-axis.

Optional for 22 -5 The Electric Field Due to a Line of Charge On the perpendicular bisector of a line of charge - 3 Aljalal-Phys 102 -142 --Ch 22 -page 27 y phys 102 -142 q total charge of q charge of dq y L r dx x

Optional for 22 -5 The Electric Field Due to a Line of Charge On the perpendicular bisector of a line of charge - 4 Aljalal-Phys 102 -142 --Ch 22 -page 28 phys 102 -142 q yq r L dx x

Optional for 22 -5 The Electric Field Due to a Line of Charge On the perpendicular bisector of a line of charge - 5 Aljalal-Phys 102 -142 --Ch 22 -page 29 phys 102 -142 What is the magnitude of the electric field for y >> L? For y >> L, The electric field is similar to that from a point charge.

Optional for 22 -5 The Electric Field Due to a Line of Charge On the line perpendicular to the end of a line of charge - 1 Aljalal-Phys 102 -142 --Ch 22 -page 30 phys 102 -142 Find the electric field at point P located on the line perpendicular to the end of a semi-infinite line of charge. y a semi-infinite rod with charge density l R q P q r dx dq to infinity x

Optional for 22 -5 The Electric Field Due to a Line of Charge On the line perpendicular to the end of a line of charge - 2 Aljalal-Phys 102 -142 --Ch 22 -page 31 phys 102 -142

Optional for 22 -5 The Electric Field Due to a Line of Charge On the line perpendicular to the end of a line of charge - 3 Aljalal-Phys 102 -142 --Ch 22 -page 32 phys 102 -142 y a semi-infinite rod with charge density l to infinity R P 450 x

22 -5 The Electric Field Due to a Line of Charge Checkpoint 3 Optional for phys 102 -142 Aljalal-Phys 102 -142 --Ch 22 -page 33 For each rod, find the direction of the net electric field at point P. -Q +Q P P +Q Solution +Q -Q

Aljalal-Phys 102 -142 --Ch 22 -page 34 22 -6 A Point Charge in an Electric Field Formula What happens when a charged particle is placed in an external electric field? q External electric field (not produced by the point charge) An electrostatic force acts on the particle External electric field

22 -6 A Point Charge in an Electric Field Direction of the force Aljalal-Phys 102 -142 --Ch 22 -page 35 External electric field (not produced by the point charge) If the charge point is positive, the force has the same direction of the electric field. If the charge point is negative, the force has the opposite direction of the electric field.

22 -6 A Point Charge in an Electric Field Checkpoint 4 -e What is the direction of the force? -e The electron initially is moving along the y-axis, what is the direction of the acceleration? Aljalal-Phys 102 -142 --Ch 22 -page 36 -e The electron initially is moving along the positive x-axis, how does its velocity change? Solution -e -e decreases

22 -6 A Point Charge in an Electric Field Ink-jet printer Aljalal-Phys 102 -142 --Ch 22 -page 37 paper Ink-Jet printing Signal from computer Ink drop generator Charging unit Deflecting plates

Aljalal-Phys 102 -142 --Ch 22 -page 38 22 -6 A Point Charge in an Electric Field Example 3 Ink drop Mass m = 1. 3 X 10 -10 kg Charge Q = - 1. 5 X 10 -13 C Initial velocity vx = 18 m/s Deflecting plates Length L =1. 6 cm Electric Field E = 1. 4 X 106 N/C What is the vertical deflection at the far edge of the plates? Solution L y Deflecting plates x

22 -7 A Dipole in an Electric Field No net force on a dipole in an external electric field Aljalal-Phys 102 -142 --Ch 22 -page 39 +q COM -q Uniform external electric field Net force on the dipole = 0 The dipole will rotate about its center of mass (COM) because of the torque on the dipole

Aljalal-Phys 102 -142 --Ch 22 -page 40 22 -7 A Dipole in an Electric Field Review - torque - 1 O O q q Torque Magnitude: t = r F sin q Direction: right-hand rule Right hand Make the index finger straight

Aljalal-Phys 102 -142 --Ch 22 -page 41 22 -7 A Dipole in an Electric Field Review - torque - 2 q q t = r F sin q torque points out of the page t = r F sin q torque points into the page Another way t = + r F sin q t = - r F sin q

Aljalal-Phys 102 -142 --Ch 22 -page 42 22 -7 A Dipole in an Electric Field Torque on a dipole in an external uniform electric field External uniform electric field +q COM -q

Aljalal-Phys 102 -142 --Ch 22 -page 43 22 -7 A Dipole in an Electric Field Derivation of the torque formula External uniform electric field r +q q COM d -q Torque t = - F r sin q - F (d - r) sin q t = - F d sin q t = - q E d sin q t = - q d E sin q t = - p E sin q

Aljalal-Phys 102 -142 --Ch 22 -page 44 22 -7 A Dipole in an Electric Field Potential energy of an electric dipole q = 00 minimum potential energy t=0 Stable equilibrium q = 900 maximum torque t=- p. E q = 1800 maximum potential energy t=0 unstable equilibrium

22 -7 A Dipole in an Electric Field Work done by an electric field on a dipole when the dipole rotates from qi to qf W = - (Uf – Ui) Aljalal-Phys 102 -142 --Ch 22 -page 45 Work done by an applied force on a dipole when the dipole rotates from qi to qf W = (Uf – Ui)

Aljalal-Phys 102 -142 --Ch 22 -page 46 22 -6 A Dipole in an Electric Field Checkpoint 5 Rank the four dipoles according to (a) the magnitude of the torque on them, and (b) their potential energy, greatest first. (1) (2) f f (3) Solution t = | p E sin q | All tie. U = -p E cos q 1 and 3 tie then 2 and 4 tie. f f (4)

22 -7 A Dipole in an Electric Field Example 4 Aljalal-Phys 102 -142 --Ch 22 -page 47 Water molecule, H 2 O, has an electric dipole of 6. 2 X 10 -30 C. m. How far apart are the molecule’s centers of positive and negative charges? Solution p =qd Oxygen atom has 8 protons and each hydrogen atom has one proton. q = 10 e H 2 O molecule is placed in an external field of 1. 5 X 104 N/C. What maximum torque can the field exert on it? Solution t = | p E sin q | maximum t = p E maximum t = (6. 2 X 10 -30 C. m)( 1. 5 X 104 N/C) = 9. 3 X 10 -26 N. m

Aljalal-Phys 102 -142 --Ch 22 -page 48 22 -7 A Dipole in an Electric Field Example 5 How much work must an external agent do to rotate a water molecule by 1800 in an electric field of 1. 5 X 104 N/C, starting from its fully aligned position for which q = 00? The water molecule has an electric dipole of 6. 2 X 10 -30 C. m. Solution W = (Uf – Ui) W = U(qf) - U(qi) initial W = -p. E cos 1800 – (-p. E cos 00 ) W = 2 p. E W = 1. 9 X 10 -25 J final