‾ The Electric Field ‾ Electric Field of a Continuous Charge Distribution‾ Electric Field Lines‾ Electric potential

Phys 2180 Lecture (2)

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18.6 The Electric Field

As we know, a charge can experience an electrostatic force due to the presence ofother charges. This surrounding Force/Coulomb is known as the Electric Field DEFINITION OF ELECRIC FIELD

The electric field that exists at a point is the electrostatic force experiencedby a small test charge placed at that point divided by the charge itself:

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SI Units of Electric Field: newton per coulomb (N/C)

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18.6 The Electric Field

Example 6 A Test Charge

The positive test charge has a magnitude of 3.0x10-8C and experiences a force of 6.0x10-8N.

(a) Find the electric field (force per coulomb) that the test charge experiences.

(b) Predict the force that a charge of +12x10-8Cwould experience if it replaced the test charge.

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(b) N1024C100.12CN0.2 88 F

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18.6 The Electric Field

It is the surrounding charges that create the electric field at a given point.

The electrostatic force points in the direction of attraction

The electric field always points away from the positive charge and towards the negative charge.

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18.6 The Electric Field

Example 7 An Electric Field Leads to a Force

The charges on the two metal spheres and the ebonite rod create an electricfield at the spot indicated. The field has a magnitude of 2.0 N/C. Determinethe force on the charges in (a) and (b)

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18.6 The Electric Field

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(b) N1048C100.24CN0.2 88 EqF o

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18.6 The Electric Field

Example 10 The Electric Field of a Point Charge

The isolated point charge of q=+15μC isin a vacuum. The test charge is 0.20m to the right and has a charge qo=+0.80μC.

Determine the electric field at point P.

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18.6 The Electric Field

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The electric field does not depend on the test charge.

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7) Electric Field Lines (lines of force)

a) Direction of force on positive charge

radial for point chargesout for positive (begin)in for negative (end)

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b) Number of lines proportional to charge

Q 2Q

c) Begin and end only on charges; never crossE?

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d) Line density proportional to field strength

Line density at radius r:

Number of lines

area of sphere

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4r2

1

r2

Lines of force model <==> inverse-square law

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Electric Field Lines

Electric field lines always begin on a positive chargeand end on a negative charge and do not stop in Mid-space.

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18.7 Electric Field Lines of two identical charges (dipoles)

The number of lines leaving a positive charge or entering a negative charge is proportional to the magnitude of the charge.

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18.7 Electric Field Lines of two different charges

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Demonstration: Van de Graff generator- purpose: to produce high field by concentrating charge -- used to accelerate particles for physics experts- principle: charge on conductors moves to the surface

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Electric Potential Energy is conservative

Gravitational force Electrostatic force

Note: Electric energy is one type of energy.

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Reference Point of Electric Potential Energy

The reference point can be anywhere. For convenience, we usually set charged particles to be infinitely separated from one another to be zero potential energy

The potential energy U of the system at any point f is

where W∞   is the work done by the electric field on a charged particle as that particle moves in from infinity to point f. 17

Electric Potential The electric potential difference V at a given

point is the electric potential energy U of a small test charge q0 situated at that point divided by the charge itself:

SI Unit of Electric Potential: joule/coulomb=volt (V) Note:•Both the electric potential energy U and the electric potential V are scalars.•The electric potential energy U and the electric potential V are not the same. The electric potential energy is associated with a test charge, while electric potential is the property of the electric field and does not depend on the test charge.

If we set        at infinity as our reference potential energy,

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The Electric Potential Difference The electric potential difference between any two points i and

f in an electric field.

Note:•Only the differences ΔV and ΔU are measurable in terms of the work W.•The is ΔV property of the electric field and has nothing to do with a test charge•The common name for electric potential difference is "voltage".

• It is equal to the difference in potential energy per unit charge between the two points.

• the negative work done by the electric field on a unite charge as that particle moves in from point i to point f.

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Notes Continue

• Electric field always points from higher

electric potential to lower electric potential.

• A positive charge accelerates from a region of

higher electric potential energy (or higher

potential) toward a region of lower electric

potential energy (or lower potential).

• A negative charge accelerates from a region

of lower potential toward a region of higher

potential.20

24.3 Electric Potential:

The potential energy per unit charge at a point in an electric field is called the electric potential V (or simply the potential) at that point. This is a scalar quantity. Thus,

If we set Ui =0 at infinity as our reference potential energy, then the electric potential V must also be zero there. Therefore, the electric potential at any point in an electric field can be defined to be

Here W∞ is the work done by the electric field on a charged particle as that particle moves in from infinity to point f.

The SI unit for potential is the joule per coulomb. This combination is called the volt (abbreviated V).

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Problem

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Example 2  Work, Electric Potential Energy, and Electric Potential

The work done by the electric force as the test charge (q0=+2.0×10–6 C) moves from A to B is WAB=+5.0×10–5 J. (a) Find the difference, ΔU=UB–UA, in the electric potential energies of the charge between these points. (b) Determine the potential difference, ΔV=VB–VA, between the points.

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Example 4  Electric Field and Electric Potential

Two identical point charges (+2.4×10–9 C) are fixed in place, separated by 0.50 m. Find the electric field and the electric potential at the midpoint of the line between the charges qA and qB.

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Electric Potential

The electrostatic force is conservative – potential energy can be defined

Change in electric potential energy is negative of work done by electric force:

2.1 Electrostatic Potential Energy and Potential Difference

Electric potential is defined as potential energy per unit charge:

Unit of electric potential: the volt (V).

1 V = 1 J/C.

2.1 Electrostatic Potential Energy and Potential Difference

Electrical sources such as batteries and generators supply a constant potential difference. Here are some typical potential differences, both natural and manufactured:

An equipotential is a line or surface over which the potential is constant.

Electric field lines are perpendicular to equipotentials.

The surface of a conductor is an equipotential.

2.2 Equipotential Surfaces

2.2 Equipotential Surfaces

Example 23-10: Point charge equipotential surfaces.

For a single point charge with Q = 4.0 × 10-9C, sketch the equipotential surfaces (or lines in a plane containing the charge) corresponding to V1 = 10V, V2 = 20V, and V3 = 30V.

2.2 Equipotential SurfacesEquipotential surfaces are always perpendicular to field lines; they are always closed surfaces (unlike field lines, which begin and end on charges).