Ch 20: Electric Charge and Electric Fields

Electric Charge

Experiments involving the rubbing of plastic, glass and wood rods with wool, silk, and other materials cause the material to inherit a property that allows for long-range attractive and repulsive forces.

Examples: • Unrolling plastic rap • Running a comb through hair • Rubbing rubber/plastic/glass rods with fur and silk • Walking on carpet with slippers

Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley

PowerPoint® Lecture prepared by Richard Wolfson

Slide 20-3

Figure 21.1

Clicker question

Conductors, insulators, and dielectrics •  Materials in which charge is free to move are conductors. •  Materials in which charge isn’t free to move are

insulators.

A metallic sphere is initially neutral. A negatively charged rod is brought in contact with a connecting rod, which is also touching the metallic sphere. What type of rod should be used such that the metallic sphere is charged?

1.  a conducting rod 2.  a insulating rod 3.  Either kind of rod will charge the sphere.

Clicker question

A negatively charged glass rod is brought near a spherical conductor, which is initially neutral. The spherical conductor is initially touching another spherical conductor which is also initially neutral. While the glass rod is near the conductor, the two conductors are separated. The glass rod is then removed. What are the charged states of the two conductors?

1.  Left is positively charged, right is negatively charged.

2.  Right is positively charged, left is negatively charged.

3.  Left is positively charged, right is neutral.

Clicker question

Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley

PowerPoint® Lecture prepared by Richard Wolfson

Slide 20-9

Figure 21.8

Coulomb’s law and the electric force •  Like charges repel, and opposite charges attract, with a

force that depends on •  The product of the two charges •  The inverse square of the distance between them

•  Mathematically, the electric force is described by Coulomb’s law:

Clicker question

12

What is the angle between to strings attached to pithballs of mass m and charge Q?

The superposition principle •  The electric force obeys the superposition principle.

•  That means the force two charges exert on a third force is just the vector sum of the forces from the two charges, each treated without regard to the other charge.

•  The superposition principle makes it mathematically straightforward to calculate the electric forces exerted by distributions of electric charge.

•  The net electric force is the sum of the individual forces.

Consider the charge configuration shown below.

CT 25.11

+q

+Q +Q

h

s/2 s/2

What is the direction of the net force on the +q charge?

A

B

C

D E

Copyright Univ. of Colorado, Boulder

A charge q is to be placed at either A or B on the mid-line of two charges +q. Will the force on q be greater at point A or at point B? A) A B) B C) Can't tell without knowing magnitude of q.

Clicker question

F =2kqQy

(a2 + y2)3/2

The electric field •  The electric field at a point in space is the force per unit

charge that a charge q placed at that point would experience:

•  The force on a charge q in an electric field is

•  The electric field is analogous to the gravitational field, which gives the force per unit mass.

Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley

PowerPoint® Lecture prepared by Richard Wolfson

Slide 20-18

Figure 21.16

Fields of point charges and charge distributions •  The field of a point charge

is radial, outward for a positive charge and inward for a negative charge.

•  The superposition principle shows that the field due to a charge distribution is the vector sum of the fields of the individual charges.

The dipole: an important charge distribution •  An electric dipole consists of two point charges of equal

magnitude but opposite signs, held a short distance apart. •  The dipole is electrically

neutral, but the separation of its charges results in an electric field.

•  Many charge distributions, especially molecules, behave like electric dipoles.

•  The product of the charge and separation is the dipole moment: p = qd.

•  Far from the dipole, its electric field falls off as the inverse cube of the distance.

Electric Dipole

phet: charges

Continuous charge distributions •  Charge is ultimately made of individual particles, but it’s

often convenient to consider it distributed continuously •  The electric field of a charge distribution follows by summing

—that is, integrating—the fields of individual charge elements dq, each treated as a point charge:

What is the vertical component, dEy, due to the little chunk of length dx? T 26.11e

x

y=H

+ + + + + + + + + + + + + + + + + + + + + ++ +

dE

dx dEy= A) B) C) D) E) |

•  The electric field of an infinite line of charge: •  The line carries charge density λ (units are C/m):

from CU Boulder

kλdx/(x2 +H2) kλx dx/(x2 +H

2)3/2

kλH dx/(x2 +H2)3/2kλH dx/(x2 +H

2)kλx dx/(x2 +H

2)

Ey =� ∞

−∞

kλy dx

(x2 + y2)3/2

Figure 21.49

The electric field at point P is

1.  kQ/a2 2.  less than kQ/a2 but greater than zero 3.  zero 4.  Depends on the value of the charge at point P

•  The electric field on the axis of a charged ring:

•  Electric field due to disk of radius R and charge Q (a distance x from center):

E =

�dERing =

�k dQRing x

(x2 + r2)3/2

E = 2πσkx1

(x2 + r2)1/2|R0

E = 2πσk

�1− x√

x2 +R2

�

E =

� R

0

k 2πσr dr x

(x2 + r2)3/2

•  Electric charge is a fundamental property of matter. •  Charge comes in two varieties, positive and negative. •  Charge is conserved. •  The force between two charges is given by Coulomb’s law:

•  The electric force obeys the superposition principle, meaning the forces due to individual charges sum vectorially.

•  The electric field describes the force per unit charge at a given point: •  The field of a dipole follows from Coulomb’s law: •  The fields of discrete charge distributions are calculated by summation. •  The fields of continuous charge distributions are calculated by integration.

•  A point charge experiences a force in an electric field. •  A dipole experiences a torque in an electric field, and a force if the

field is not uniform.

Summary