MUATAN dan MEDAN LISTRIK Yohanes Edi Gunanto Muatan

MUATAN dan MEDAN LISTRIK Yohanes Edi Gunanto

Muatan Listrik ¡ Two types of charges exist l l 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 ¡ l Protons do not move from one material to another because they are held firmly in the nucleus

Attractive force Repulsive force

Asal muatan ¡ ¡ ¡ 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 ~ 10 -15 m (femtometer) Atomic diameter ~ 10 -9 m (nanometer)

Classes of Materials o o o 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= 1. 602 x 10 -19 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 ini sulit dimungkinkan karena secara teori tidak ada quark bebas.

Principle of Superposition ¡ For a system of N charges q 1, q 2, q 3, …, q. N, the resultant force F 1 on q 1 exerted by charges q 2, q 3, …, q. N is: • Each charge may be considered to exert a force on q 1 that is independent of the other charges present.

Contoh soal : Hitung besar gaya listrik pada sebuah elektron dalam atom hidrogen (karena tertarik oleh sebuah proton, Q 2 = e). Jarak rata-rata proton-elektron: 0, 53 x 10 -10 m Jawab: Q 1 = - e = - 1, 6 x 10 -19 C Q 2 = e = 1, 6 x 10 -19 C r = 0, 53 x 10 -10 m tanda negatif berarti attraktif. (Kemana arah gaya? gaya pada elektron mengarah ke proton)

Hitung gaya (net gaya) yang bekerja pada Q 3 dari gambar berikut karena dua muatan yang lain.

Electric Field

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

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

Electric Field Line Patterns n n 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 q 0 :

The electric force on a positive test charge q 0 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 l l l 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? 2 q a a a 3 q q a 4 q

Electric Field ON axis of dipole -q a +q P x

p = qa “dipole moment” -- VECTOR - +

What if x>> a? (i. e. very far away) E~p/r 3 is actually true for ANY point far from a dipole (not just on axis)

Electric Dipole in a Uniform Field l l l 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 l = |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 d. Q, each producing an electric field d. E: ε 0 = permittivity of free space

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

Example: Field on Bisector of Charged Rod n n n 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 P y a x dx o L dx q

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

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

l 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

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

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