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FISIKA DASAR

Listrik Magnet

Djati Handoko

Departemen Fisika UI

djati@fisika.ui.ac.id, djati.handoko@ui.ac.id

08129789507

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Silabus Listrik

• Physics for Scientists and Engineers, 6th Edn[1]. (R.A.Serway, J.W.Jewett, Thomson 2004, ISBN 0534408427)

• Medan Listrik:

– Distribusi Muatan Diskrit

– Distribusi Muatan Kontinu

• Potensial Listrik

• Kapasitansi, Dielektrik, dan Energi Elektrostatik

• Arus Listrik

• Rangkaian Arus Searah

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• Medan Magnetik

• Sumber Medan Magnetik

• Induksi Magnetik

• Magnetisme Dalam Materi

• Rangkaian Arus Bolak Balik

• Persamaan Maxwell dan GelombangElektromagnetik

Silabus Magnet

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Electric Fields

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Properties of Electric Charges

• In a series of simple experiments, it was found that there are two kinds of electric charges, which were given the names positive and

negative by Benjamin Franklin (1706–1790).

• charges of the same sign repel one another and charges with

opposite signs attract one another.

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Properties of Electric Charges

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Charging Objects By Induction

Charging a metallic object by induction (that is, the two

objects never touch each other).

(a) A neutral metallic sphere, with equal numbers of positive and negative charges.

(b) The electrons on the neutral sphere are redistributed when a charged rubber rod is placed near the sphere.

(c) When the sphere is grounded, some of its electrons leave throughthe ground wire.

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(d) When the ground connection is removed, the sphere has excess positive charge that is non uniformly distributed.

(e) When the rod is removed, the remaining electrons redistribute uniformly and there is a net uniform distribution of positive charge

on the sphere.

Charging Objects By Induction

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Coulomb’s Law

• The electric force:

– is inversely proportional to the square of the separation r between the particles and directed along the line joining them;

– is proportional to the product of the charges q1 and q2 on the two particles;

– is attractive if the charges are of opposite sign and repulsive if the charges have the same sign;

– is a conservative force.

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Coulomb’s Law

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Some applications

painting static charge

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Quick Quiz

Object A has a charge of +2 µC, and object B has a charge of +6 µC. Which statement is true about the electric forces on the objects?

– (a) FAB = -3FBA

– (b) FAB = -FBA

– (c) 3FAB = -FBA

– (d) FAB = 3FBA

– (e) FAB = FBA

– (f) 3FAB = FBA

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example

• Consider three point charges located at the corners of a right triangle as shown in figure, where q1= q3 = 5.0 µC, q2 =-2.0 µ C, and a =

0.10 m. Find the resultant force exerted on q3.

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quizDua buah bola bermuatan identik masing-masing memiliki massa 3 x 10-2 kg digantung dalam keadaan setimbang seperti terlihat pada gambar. Panjang kawat L = 15 cm dengan sudut θ = 5o. Tentukanlah :

– Besarnya muatan masing-masing bola

– Seandainya temanmu mengajukan masalah ini dengan asumsi kedua muatan tidak identik. Ia mengklaim bahwa kondisi simetri seperti pada gambar tidak akanterpenuhi karena muatan tidak sama, sehingga sudut yang dibentuk kawat akanberbeda. Akibatnya problem yang harus diselesaikan jadi jauh lebih sulit,bagaimana pendapat kamu

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The Electric Field

An electric field is said to exist in the region of space around a charged object (the source charge). When another charged object

(the test charge) enters this electric field, an electric force acts on it.

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A small positive test charge qo placed near an object carrying a much larger positive charge Q experiences an electric field E directed as

shown.

The Electric Field

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A test charge q0 at point P is a distance r from a

point charge q.

(a) If q is positive, then the force on the test charge is directed away from q.

(b) For the positive source charge, the electric field at P points radiallyoutward from q.

(c) If q is negative, then the force on the test charge is directed toward q.

(d) For the negative source charge, the electric field at P points radiallyinward toward q.

The Electric Field

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at any point P, the total electric field due to a group of source charges equals the vector sum of the electric fields of all the charges.

The Electric Field

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• A charge q1 = 7.0 µC is located at the

origin, and a second charge q2 = -5.0 µC is located on the x axis,

0.30 m from the origin. Find the electric field at the point P, which has

coordinates (0, 0.40) m.

example

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The electric field at P due to a continuous charge distribution is the vector sum of the

fields ∆E due to all the elements ∆q of the

charge distribution.

Electric Field of a ContinuousCharge Distribution

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• The total electric field at P due to all elements in the charge distribution is approximately

• Electric field due to a continuous charge distribution

• When performing such calculations, it is convenient to use the

concept of a charge density along with the following notations:

• If the charge is nonuniformly distributed over a volume, surface, or

line, the amounts of charge dq in a small volume, surface, or length

element are

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• A rod of length l has a uniform positive charge per unit length λ and a

total charge Q. Calculate the electric field at a point P that is located

along the long axis of the rod and a distance a from one end

Example: The Electric Field Due to a Charged Rod

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• The field dE at P due to this segment is in the negative x direction (because the source of the field carries a positive charge), and its

magnitude is

• The total field at P due to all segments of the rod, which are at

different distances from P, is given by equation before, which in this

case becomes

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• The electric field vector E is tangent to the electric field line at each point. The line has a direction, indicated by an arrowhead, that is the

same as that of the electric field vector.

• The number of lines per unit area through a surface perpendicular to

the lines is proportional to the magnitude of the electric field in that

region.

Electric Field Lines

Electric field lines penetrating two surfaces.

The magnitude of the field is greater on

surface A than on surface B.

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rules

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• When a particle of charge q and mass m is placed in an electric field E, the electric force exerted on the charge is qE

• The acceleration of the particle is therefore

Motion of Charged Particles in a Uniform Electric Field

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• A positive point charge q of mass m is released from rest in a uniform electric field E directed along the x axis, as shown in figure. Describe

its motion (726).

An Accelerating Positive Charge

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• Electrons leaving the cathode C are accelerated to the anode A. In addition to accelerating electrons, the electron gun is also used to

focus the beam of electrons, and the plates deflect the beam.

The Cathode Ray Tube

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• A small, 2.00-g plastic ball is suspended by a 20.0-cm-long string in a

uniform electric field as shown in figure. If the ball is in equilibrium when the string makes a 15.0° angle with the vertical, what is the net

charge on the ball?

quiz