MUATAN dan MEDAN LISTRIK

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MUATAN dan MEDAN LISTRIK
Yohanes Edi Gunanto

Muatan Listrik Two types of charges exist
They are called positive and negative Named by Benjamin Franklin Like charges repel and unlike charges attract one another Nature’s basic carrier of positive charge is the proton Protons do not move from one material to another because they are held firmly in the nucleus

Attractive force Repulsive force

Asal muatan Nuclear diameter ~ 10-15 m (femtometer)
Atoms consist of a nucleus containing positively charged protons. The nucleus of an atom is surrounded by an equal number of negatively charged electrons. The net charge on an atom is zero. An atom may gain or lose electrons, becoming an ion with a net negative or positive charge. Polar molecules have zero net charge but their charges are unevenly distributed in space (e.g. water). Nuclear diameter ~ m (femtometer) Atomic diameter ~ 10-9 m (nanometer)

Classes of Materials CONDUCTORS are materials in which charges may move freely (e.g. copper). INSULATORS are materials in which charges cannot move freely (e.g. glass). SEMICONDUCTORS are materials in which charges may move under some conditions (e.g. silicon).

Bagaimana muatan diukur ?
elektroskope / elektrometer

Hukum Coulomb For charges in a VACUUM k =

Quantum of Electric Charge
Electric charge is quantized. The smallest possible unit is the charge on one electron or one proton: e= x Coulombs No smaller charge has ever been detected in an experiment. Catatan kecil: Ahli Fisika partikel elementer (juga ahli Fisika energi tinggi, 1963) berteori bahwa ada partikel yang lebih kecil, disebut quark, yang mempunyai muatan 2/3 e atau 1/3 e. Deteksi eksperimen secara langsung pada partikel-partikel ini sulit dimungkinkan karena secara teori tidak ada quark bebas.

Principle of Superposition
For a system of N charges q1, q2, q3, …, qN, the resultant force F1 on q1 exerted by charges q2, q3, …, qN is: Each charge may be considered to exert a force on q1 that is independent of the other charges present.

tanda negatif berarti attraktif.
Contoh soal : Hitung besar gaya listrik pada sebuah elektron dalam atom hidrogen (karena tertarik oleh sebuah proton, Q2 = e). Jarak rata-rata proton-elektron: 0,53 x m Jawab: Q1 = - e = - 1,6 x C Q2 = e = 1,6 x C r = 0,53x10-10 m tanda negatif berarti attraktif. (Kemana arah gaya? gaya pada elektron mengarah ke proton)

Hitung gaya (net gaya) yang bekerja pada Q3 dari gambar berikut karena dua muatan yang lain.

Electric Field

Electric Field Line Patterns
Point charge The lines radiate equally in all directions For a positive source charge, the lines will radiate outward

Electric Field Line Patterns
For a negative source charge, the lines will point inward

Electric Field Line Patterns
An electric dipole consists of two equal and opposite charges The high density of lines between the charges indicates the strong electric field in this region

Electric Field The ELECTRIC FIELD E is defined in terms of the electric force that would act on a positive test charge q0 :

The electric field at a distance r from a single charge q:
The electric force on a positive test charge q0 at a distance r from a single charge q: The electric field at a distance r from a single charge q:

Electric Field due to a Group of Charges:

Example Problem Four point charges are at the corners of a square of side a as shown. Determine the magnitude and direction of the electric field at the location of q. What is the resultant force on q? 2q q a a a a 3q 4q

Electric Field ON axis of dipole
-q +q

p = qa “dipole moment” -- VECTOR

What if x>> a? (i.e. very far away)
E~p/r3 is actually true for ANY point far from a dipole (not just on axis)

Electric Dipole in a Uniform Field
Net force on dipole = 0; center of mass stays where it is. Net TORQUE t: INTO page. Dipole rotates to line up in direction of E. | t | = 2(QE)(d/2)(sin q) = (Qd)(E)sinq = |p| E sinq = |p x E| The dipole tends to “align” itself with the field lines. Distance between charges = d

Electric Field from Continuous Charge Distributions
If a total charge Q is distributed continuously, it may be sub-divided into elemental charges dQ, each producing an electric field dE: ε0 = permittivity of free space

Uniform Charge Distributions
Volume Charge Density: ρ=Q/V Surface Charge Density: σ=Q/A Linear Charge Density: λ=Q/l l = Q/L r = Q/V s = Q/A

Example: Field on Bisector of Charged Rod
q L a P o y x dx Uniform line of charge +Q spread over length L What is the direction of the electric field at a point P on the perpendicular bisector? (a) Field is 0. (b) Along +y (c) Along +x Choose symmetrically located elements of length dx x components of E cancel

Line Of Charge: Field on bisector
Distance Q L a P o x dE dx d Charge per unit length

What is E very far away from the line (L<<a)?
What is E if the line is infinitely long (L >> a)?

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. Start with

Then : Finalize l => 0 ? a >> l ?

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