The Electric Field and Gauss’s Law

BUDI ARIFVIANTO

Department of Mechanical EngineeringGadjah Mada University, Yogyakarta, INDONESIA

The electric field

F = E.q’

• A general formulation to quantify the existence of electrical influence…

• It can be calculated by placing point of charge with which the electrostatic force is apparent… subsequently, find the ratio of the force and the charge

• Electric field is a vector quantity as well as the electrostatic force…

Calculation of Electric Field

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20

4

1

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4

1

r

q

q

FE

r

qqF

2

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r

rqE

r

The direction of the field is away from the charge q if the latter is positive, toward q if it is negative.

The direction of the electric field caused by a point charge is represented conveniently by use of unit vectors.

r is the distance from the charge to point P. When q is negative, the

direction of E is toward q, opposite to

vector

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1

...

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11

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21

r

rq

r

rqE

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Study case 1

Point charges:

q1 = +12 x 10-9C (lower left), q2 = -12 x 10-9C (lower right),

r = 10 cm

Find E at point P!

Calculation of electric field: the sum of electric segments[Study case 2 is inserted]

204

1

r

rqE

2

04

1

r

dqrE

The limit of integration must be assigned so as to include all charges contributing to the field.

Study case 2: Find the model of electric field at a distance z above the midpoint of a straight line segment of length 2L which carries a uniform line charge! (Model of a transmission line)

z

Field Lines

A field line (in a electric field) is an imaginary line drawn in such a way that its direction at any point (i.e., the direction of its tangent) is the same as the direction of the field at that point. See figure…

The concept of field lines was introduced by Michael Faraday (1791-1867) as an aid in visualizing electric (and magnetic) field.

Gauss’s Law

0q

EA

Karl Friedrich Gauss (1777-1855) was a German scientist and mathematician who made many contribution to experimental and theoretical physics and to mathematics.

Gauss’ Law: The net flux through any closed surface is proportional to the net charge enclosed by that surface, i.e.,

Permittivity is a physical quantity that describes how an electric field affects and is affected by a dielectric medium, and is determined by the ability of a material to polarize in response to the field, and thereby reduce the field inside the material. Thus, permittivity relates to a material's ability to transmit (or "permit") an electric field.

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2

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r

qq

r

qqkF

Recall the Coulomb’s law:

Electric flux

About the flux…Compare the water flux in the following three situations. Rank the flux in cases (a), (b), and (c), from largest to smallest.

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1

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Applications of Gauss’s law

• Location of excess charge on a conductor• Coulomb’s law• Field of a charged conducting sphere• Field of a line charge and of a charged

cylindrical conductor• Field of an infinite plane sheet of charge• Field of an infinite plane charged conducting

plate• Field between oppositely charged parallel

conducting plates• Field just outside any charged conductor