PHY 102: Lecture Concept of Electric Field 2.2 Electric Field Defined 2.3 Electric Field Lines 2.4 Electric Field in Conductor

PHY 102: Lecture 2 Electric Field 2.1 Concept of Electric Field

Concept of Electric Field - 1 Electric force, like gravity, is a long-range force No contact is required for one charged particle to exert a force on another charged particle In a process called action at a distance, the force is transmitted through empty space The concept of action at a distance greatly troubled many of the leading thinkers of Newton’s day Force, they believed, should have some mechanism by which it is exerted The idea of action at a distance, with no apparent mechanism, was more than most scientists could accept

Concept of Electric Field - 2 The great prestige and success of Newton was able to keep scientists’ doubts in check At the end of the 18 th century, investigations of electric phenomena reopened the issue of action at a distance

Concept of Electric Field - 3 Given charged particles A and B The particles have been at rest for a long period of time, we can use Coulomb’s law to determine the force that A exerts on B Charge A suddenly starts moving In response, force on B must pivot to follow A Does this happen instantly? Is there some delay between A moving and when the force on B responds?

Concept of Electric Field - 4 Neither Coulomb’s Law nor Newton’s law of gravity is dependent upon time So the answer has to be “instantly” Most scientists found this troubling What if A is 100,000 light years from B? Will B respond instantly to an event 100,000 light years away? The idea of instantaneous transmission of forces was becoming unbelievable to most scientists by the beginning of the 19 th century

Concept of Electric Field - 5 If there is a delay, how long is it? How does the information to “change force” get sent from A to B? These were the issues when a young Michael Faraday appeared on the scene

Michael Faraday (1791 – 1867) Son of a poor blacksmith Sent to work at an early age with almost no formal education Found employment with a printer and bookbinder He began to read the books that came through the shop A customer brought in a copy of the Encyclopedia Britannica to be rebound Faraday discovered a lengthy article about electricity He was never able to become fluent in mathematics Faraday developed many ingenious pictorial methods for thinking about and describing physical phenomena The most important of these was the field

Concept of Electric Field - 6 Faraday suggested that the space itself around charge A is filled with some kind of electric influence Charge A in someway alters the space around it In this view, charge B near charge A responds not directly to charge A but, instead, to the alteration of space caused by charge A This space alteration, whatever it is, is the mechanism by which the long-range force is exerted

Concept of Electric Field - 7 Faraday’s idea came to be called a field The charge makes an alteration everywhere in space Other charges then respond to the alteration at their position The space around a charge is altered to create the electric field

Concept of Electric Field - 8 Faraday’s idea was not taken seriously at first It seemed too vague and non-mathematical to scientists involved in the Newtonian tradition of particles and forces The significance of the concept of field grew as electromagnetic theory developed during the first half of the 19 th century What seemed at first a pictorial “gimmick” came to be seen as more and more essential for understanding electric forces Faraday’s field ideas were finally placed on a firm mathematical foundation in 1865 by James Clerk Maxwell

The Field Model Describes how two charges interact 1.Some charges, which we will call the source charges, alter the space around them by creating and electric field 2.A separate charge in the electric field experiences a force exerted by the field

PHY 102: Lecture 2 Electric Field 2.2 Electric Field Defined

Definition of Electric Field Vector The electric field that exits at a point is the electrostatic force experienced by a small test charge q 0 placed at that point divided by the charge itself The magnitude of the electric field is: E = F/q 0 Electric field direction is the same as the direction of the force on a positive test charge SI Unit of Electric Field: Newton per coulomb (N/C)

Electric Force/Field - 1

Electric Force/Field - 2

Electric Field – Point Charge q Magnitude Direction –If q is positive, E field is directed away from q –If q is negative, E field is directed toward q

Electric Field – Parallel Plate Capacitor This device consists of two parallel metal plates, each with area A A charge +q is spread uniformly over the one plate A charge –q is spread uniformly over the other plate In the region between the plates and away from the edges, the electric field points from the positive plate toward the negative plate and is perpendicular to both σ denotes the charge per unit area (σ = q/A) and is sometimes called the charge density. Except in the region near the edges, the field has the same value at all places between the plates The field does not depend on the distance from the charges

Problem A positive test charge is q 0 = +3.0 x C Test charge feels force of F = 6.0 x N (a) Find the magnitude of the electric field (force per coulomb) that test charge feels (b) Predict force that charge of +12x10 -8 C feels if it replaced q 0

Problem (a) Force per coulomb of test charge is field E (b) Force on charge of Q = +12 x C F = QE

Problem There is an isolated point charge of q = +15  C in a vacuum. Using a test charge of q 0 =  C, determine the electric field at point P, which is 0.20m away

Problem Coulomb’s Law gives the magnitude of the force between q and q 0 Definition of the magnitude of the electric field gives The electric field points in the same direction as the force on the positive test charge

Problem Two positive point charges q 1 = +16  C and q 2 = +4.0  C Separated by a distance of 3.0 m Find the spot on the line between the charges where the net electric field is zero

Problem Between the charges the two field contributions have opposite directions The net electric field is zero at the place where the magnitude of E 1 equals that of E 2

PHY 102: Lecture 2 Electric Field 2.3 Electric Field Lines

Electric charges create an electric field in space It is useful to have a kind of “map” that gives the direction and strength of the field at various places Electric field lines provide such a map A positive test charge would experience a repulsive force Electric field created by the charge +q is directed radially outward The lines begin on the charge +q and point radially outward Electric field lines are always directed away from positive charges and toward negative charges Number of lines is chosen to be proportional to magnitude of charge No matter how many charges are present, the number of lines per unit area passing perpendicularly through a surface is proportional to the magnitude of the electric field

Properties of Electric Field Lines Tangent to a field line at any point is in the direction of the electric field at that point The field lines are closer together where the electric field strength is larger Every field line starts on a positive charge and ends on a negative charge Field lines cannot cross

Electric Field Line Development - 1 Start with a positive point charge at the middle of the origin Show the electric force field arrows

Electric Field Line Development - 2 Start at some point and begin to draw lines Start by drawing a line in the direction of the local arrow When you get to the next arrow draw the line in that direction

Electric Field Line Development - 3 You obtain the diagram on the side Looks like the spokes of a wheel Called a radial electric field Number of lines you draw is up to you

Electric Field Lines – Single “+” Charge Electric field lines are radially outward If electric field lines are close, the field is strong As the electric field lines get further apart, the field gets weaker

Electric Field Lines – Single “-” Charge

Electric Field Lines – “+” and “-” Charges Field lines for positive and negative charges Field lines are in the direction of force on positive test charge Field lines are directed away from positive charges Field lines are directed towards negative charges

Electric Field Lines – “+” and “+” Charges

Electric Field Lines – Parallel Plates

PHY 102: Lecture 2 Electric Field 2.4 Electric Field In Conductor

Electric Field Inside Conductor - 1 In conducting materials (copper), charges move easily in response to forces that electric fields exert Suppose that a piece of copper carries a number of excess electrons somewhere inside Each electron would experience a force of repulsion because of the electric field of its neighbors Since copper is a conductor, the excess electrons move readily in response to that force They rush to the surface of the copper Once static equilibrium is established with all of the excess charge on the surface, no further movement of charge occurs At equilibrium under electrostatic conditions, any excess charge resides on the surface of a conductor

Electric Field inside Conductor - 2 Consider the interior of the copper The interior is electrically neutral, although there are still free electrons that can move under the influence of an electric field The absence of a net movement of these free electrons indicates that there is no net electric field present within the conductor The excess charges arrange themselves on the conductor surface precisely in the manner needed to make the electric field zero within the material At equilibrium under electrostatic conditions, the electric field is zero at any point within a conducting material

Electric Field inside Conductor - 3 An uncharged, solid cylindrical conductor at equilibrium is in the central region of a parallel plate capacitor Induced charges on the surface of the cylinder alter the electric field lines of the capacitor Since an electric field cannot exist within the conductor under these conditions, the electric field lines do not penetrate the cylinder Instead, they end or begin on the induced charges A test charge placed inside the conductor would feel no force due to the presence of the charges on the capacitor The conductor shields any charge within if from electric fields created outside the conductor

Electric Field inside Conductor - 4 The electric field just outside the surface of a conductor is perpendicular to the surface at equilibrium under electrostatic conditions If the field were not perpendicular, there would be a component of the field parallel to the surface Since the free electrons on the surface of the conductor can move, they would do so under the force exerted by that parallel component In reality, however, no electron flow occurs at equilibrium Therefore, there can be no parallel component, and the electric field is perpendicular to the surface

Electric Field inside Conductor - 6 The electric field is zero inside a conductor Nothing is disturbed if a cavity is cut from the interior of the material Interior of the cavity is also shielded from external electric fields This has important applications for shielding electronic circuits To eliminate such interference, circuits are often enclosed within metal boxes that provide shielding from external fields