15_Electric Field

Chapter 15 Lecture

The Electric Field

Prepared by

Dedra Demaree,

Georgetown University

The Electric Field

• _{Why is it safe to sit in a car during a lightning}

Be sure you know how to:

• _{Find the force that one charged object exerts on}

another charged object (Section 14.4).

• _{Determine the electric potential energy of a}

system (Section 14.5).

• _{Explain the differences in the internal structure}

of electric conductors and dielectrics (Section 14.3).

What's new in this chapter

• _{We learned how to describe electrostatic}

interactions in two ways: with a force exerted by one charged object on another and with the

electric potential energy.

– _{This is only the second interaction we have}

encountered where forces are exerted

without the objects being in direct contact.

• _{How does one charged object "know" about the}

A model of the mechanism for electrostatic

interactions

• _{A model for electric}

interactions, suggested by Michael Faraday, involves some sort of electric

disturbance in the region surrounding a charged object.

• _{Physicists call this electric}

disturbance an electric field.

Gravitational field due to a single

object with mass

• _{We find a mathematical description of the "strength" of}

Electric field due to a single point-like

charged object

• _{We use a similar approach of test charges to}

construct a physical quantity for the "strength" of the electric field:

Electric field due to a single point-like

charged object

• _{We can interpret this field as follows:}

• _{The E field vector at any location points away}

from the object creating the field if Q is positive, and toward the object creating the field if Q is negative.

Observational experiment

Superposition principle

• _{When multiple charged objects are present,}

each object makes its own contribution to the E

Using the superposition principle

Conceptual Exercise 15.1

• _{The muscles of the heart continually contract}

and relax, making the heart an electric dipole with equal-magnitude positive and negative

electric charges. Estimate the direction of the E

E

field lines

E

field lines

• _{E field lines point away from an area of positive}

charge and point toward an area of negative charge.

• _{Closer to the charged objects, the lines are}

Tip

Tip

Conceptual Exercise 15.2

• _{Draw E field lines for a large, uniformly charged}

Determining the

E

field produced

by given source charges

Example 15.3

• _{Two small metal spheres attached to insulating}

stands reside on a table a distance d apart. The left sphere has positive charge +q and the right sphere has negative charge −q. Determine the magnitude and direction for the E field at a

Problem-solving strategy: Incorporating the

E

field into Newton's second law

• _{In the "Simplify and diagram" step, be sure to}

determine the E field produced by the

environment. Is it produced by point-like charges (making it nonuniform) or by large charged

plates (making it uniform)?

Example 15.5

• _{Inside an inkjet printer, a tiny ball of black ink of}

mass 1.1 x 10−11 kg with charge −6.7 x 10−12 C

moves horizontally at a speed of 40 m/s. The ink ball enters an upward-pointing uniform E field of magnitude 1.0 x 104 N/C produced by a

negatively charged plate above and a positively charged plate below. The plates deflect the ink ball so that it lands at a particular spot on a

The

V

field

• _{Can we describe electric fields using the}

concepts of work and energy?

• _{To do so, we need to describe the electric field}

not as a force-related E field, but as an energy-related field.

Tip

The superposition principle and the

V

field

due to multiple charges

– where Q₁, Q₂, Q₃, … are the source charges

(including their signs) creating the field and r₁,

r₂, r₃, … are the distances between the source charges and the location where we are

Quantitative Exercise 15.6

• _{Suppose that the heart's dipole charges −Q and}

+Q are separated by distance d. Write an

expression for the V field due to both charges at point A, a distance d to the right of the +Q

charge.

1. Simplify and diagram.

2. Represent mathematically.

Finding the electric potential energy when

the

V

field is known

• _{If we know the electric potential at a specific}

location, we can rearrange the definition of the V

Potential difference

• _{The value of the electric potential depends on}

the choice of zero level, so we often use the difference in electric potential between two points.

Particles in a potential difference

• _{A positively charged object accelerates from}

regions of higher electric potential toward

regions of lower potential (like an object falling to lower elevation in Earth's gravitational field).

• _{A negatively charged particle tends to do the}

Example 15.7

• _{Inside an X-ray machine is a wire (called a}

filament) that, when hot, ejects electrons.

Imagine one of those electrons, now located

outside the wire. It starts at rest and accelerates through a region where the V field increases by 40,000 V. The electron stops abruptly when it hits a piece of tungsten at the other side of the region, producing X-rays. How fast is the

electron moving just before it reaches the tungsten?

Equipotential surfaces: Representing

the

V

field

• _{The lines represent surfaces of constant electric}

potential V, called equipotential surfaces.

• _{The surfaces are spheres (they look like circles}

Equipotential surfaces and

E

field

Deriving a relation between the

E

field and

Δ

V

• _{We attach a small object with}

charge +q to the end of a very thin wooden stick and place

the charged object and stick in the electric field produced by the plate.

• _{The only energy change is the}

system's electric potential

energy, because the positively charged object moves farther away from the positively

charged plate.

Deriving a relation between the

E

field and

Δ

V

• _{Applying the generalized work-energy equation,}

we get:

• _{Equivalently, the component of the E field along}

Conceptual Exercise 15.8

• _{Can you think of locations relative to charge}

distributions where:

1. The V field at a particular location is zero but the E field is not?

2. The E field is zero but the V field is not zero?

Electric field of a charged conductor

• _{Free electrons in a conductor are quickly}

redistributed until equilibrium is reached, at

which point the E field inside the conductor and parallel to its surface becomes zero.

Grounding

• _{Grounding discharges}

an object made of

conducting material by connecting it to Earth.

• _{Electrons will move}

between and within the spheres until the V field on the surfaces of and within both spheres

achieves the same value.

Uncharged conductor in an electric field:

Shielding

• _{The free electrons inside the object become}

redistributed due to electric forces, until the E

Uncharged conductor in an electric field:

Shielding

• _{The interior is protected from the external field—}

an effect called shielding.

Dielectric materials in an electric field

• _{If an atom in a dielectric material}

resides in a region with an external electric field, the

nucleus and the electrons are displaced slightly in opposite

Polar water molecules in an external electric

field

• _{Some molecules, such as water, are natural}

electric dipoles even when the external E field is zero.

E

field inside a dielectric

• _{A dielectric material cannot completely shield its}

E

field inside a dielectric

• _{Physicists use a physical quantity to characterize}

the ability of dialectrics to decrease the E field:

– _{The dielectric constant κ} –

Electric force and dielectrics

• The force that object 1 exerts on object 2 is reduced by

κ compared with the force it would exert in a vacuum.

• Inside the dielectric material, Coulomb's law is now written as:

Salt dissolves in blood but not in air

• _{When salt is placed in water or blood:} – _{Many more collisions occur between}

molecules than between molecules and air; these can break an ion free from the crystal.

– _{Any ions that become separated do not exert}

nearly as strong as an attractive force on each other because of the dielectric effect.

– _{The random kinetic energy of the liquid is}

Tip

Capacitors

• _{A capacitor consists of two conducting surfaces}

separated by a nonconducting material.

• _{The role of a capacitor is to store electric potential}

Capacitors

(Cont'd)

Capacitors

• _{If we consider the capacitor plates to be large}

flat conductors, charge should be distributed evenly on the plates.

– _{The magnitude of the E field between the}

plates relates to the potential difference from one plate to the other and the distance

separating them

– _{To double the E field, the charge on other}

Capacitors

• _{The proportionality constant C in this equation is}

called the capacitance of the capacitor.

• _{The unit of capacitance is 1 coulomb/volt = 1 farad}

(in honor of Michael Faraday).

Capacitance of a capacitor

• _{A capacitor with larger-surface-area plates}

should be able to maintain more charge

Capacitance of a capacitor

• _{A larger distance between the plates leads to a}

smaller-magnitude E field between the plates. Because the

magnitude of this E field is proportional to the amount of electric charge on the plates, a larger plate separation leads to a smaller-magnitude electric charge on the plates.

Capacitance of a capacitor

• _{Material between the plates with a large}

dielectric constant becomes polarized by the electric field between the plates. Thus more charge moves onto capacitor plates that are

Capacitance of a capacitor

• _{The capacitance of a particular capacitor should}

increase if the surface area A of the plates

increases, decrease if the distance d between them is increased, and increase if the dielectric constant k of the material between them

increases:

Quantitative Exercise 15.9

• _{Estimate the capacitance of your physics}

textbook, assuming that the front and back covers (area A = 0.050 m2, separation d = 0.040 m) are

made of a conducting material. The dielectric constant of paper is approximately 6.0.

• _{Determine what the potential difference must be}

across the covers for the textbook to have a

charge separation of 10−6 C (one plate has charge

+10−6 C and the other has charge −10−6 C).

Body cells as capacitors

• _{Cells, including nerve cells, have capacitor-like}

properties.

– _{The conducting "plates" are the fluids on}

either side of a moderately nonconducting cell membrane.

– _{In this membrane, chemical processes cause}

ions to be "pumped" across the membrane.

– _{As a result, the membrane's inner surface}

Example 15.10

• _Estimate:

1. The capacitance C of a single cell.

2. The charge separation q of all of the

membranes of the human body's 1013 cells.

• Assume that each cell has a surface area of

A = 1.8 x 10−9 m2, a membrane thickness of d = 8.0 x 10−9 m, ΔV = 0.070 across the

membrane wall, and a membrane dielectric constant κ = 8.0.

Energy of a charged capacitor

• _{To determine the electric}

potential energy in a charged capacitor, we start with an

uncharged capacitor and then calculate the amount of work that must be done on the

Energy of a charged capacitor

• _{The process of charging a capacitor is similar to}

stretching a spring: at the beginning, a smaller force is needed to stretch the spring by a certain amount compared to the much greater force

needed when the spring is already stretched.

Quantitative Exercise 15.11

• _{In Example 15.10, we estimated that the total}

Energy density of electric field

• _{To have a measure of energy independent of}

the capacitor volume, we will use the physical quantity of energy density.

– _{This energy density quantifies the electric}

potential energy stored in the electric field per cubic meter of volume.

–

Tip

Electrocardiography

• _{An electric charge separation occurs when muscle cells}

in the heart contract during the pumping process.

• _{As each muscle cell contracts, positive and negative}

Conceptual Exercise 15.12

• _{The first figure shows a simplified electric dipole charge}

distribution on a heart at one instant during a heartbeat and two ECG pads on opposite shoulders of the person's body. What will these pads measure at that particular

instant?

– _{Draw E field vectors produced by the heart's dipole}

charge, representing the electric field at the location of the dot in the figure.

– _{Determine the direction of the forces exerted by the}

electric field on a positive sodium ion and on a negative chlorine ion in the body tissue at that location.

Lightning

• _{When the E field in air or in some other material is very}

large, free electrons accelerate and quickly acquire

Lightning rods

• _{Dielectric breakdown}

occurs between the cloud and the lightning rod.

• _{Drawing lightning to the}

rod and away from the

building prevents damage to the building and its

inhabitants.

Summary

Summary