Risdawati Butarbutar, ST - SMAN2 Soposurung Balige

Electrostatics

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Risdawati Butarbutar, ST - SMAN2

Soposurung Balige

PROPERTIES OF ELECTRIC CHARGES

Two kinds of charges occur in nature, with the property that unlike charges attract one another and like charges repel one another. [Benjamin Franklin (1706–1790)]

Charge is conserved when one object is rubbed against another, charge is not created in the process. The electrified state is due to a transfer of charge from one object to the other. [Benjamin Franklin (1706–1790)]

Charge is quantized electric charge always occurs as some integral multiple of a fundamental amount of charge e ( q = n x e ). [Robert Millikan (1868–1953)]

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Risdawati Butarbutar, ST - SMAN2 Soposurung Balige

COULOMB’S LAW

Coulomb’s experiments showed that the electric force between two stationary charged particles

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.

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r

qqkF

Coulomb’s law the magnitude of the electric force (sometimes called the Coulomb force) between two point charges:

k : Coulomb constant (8.987 x 109 Nm2/C2 )q : charge ( Coulomb )r : separation distance ( m )

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Example :1. The electron and proton of a

hydrogen atom are separated (on the average) by a distance of approximately 5.3 x 10-11 m. Find the magnitudes of the electric force and the gravitational force between the two particles.

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2. Consider three point charges located at the corners of a right triangle as shown in figure, where q1 = q3 = 5μC, q2 = -2μC and the perpendicular side is 0.10 m. Find the resultant force exerted on q3 .

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Exercise :1. Consider two conducting balls both of mass

m and equal charge q suspended by nonconducting cords of equal length, l as shown in Figure below. How does the separation of the balls depend on charge, mass, and length?

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2. In the Bohr theory of the hydrogen atom, an electron moves in a circular orbit about a proton, where the radius of the orbit is 0.529 x 10-10 m(a) Find the electric force between the

two.(b) If this force causes the centripetal

acceleration of the electron, what is the speed of the electron?

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3. A long, nonconducting, massless rod of length L, pivoted at its center and balanced with a block of weight W at a distance x from the left end. At the left and right ends of the rod are attached small conducting spheres with positive charges q and 2q, respectively. A distance h directly each of these spheres is a fixed sphere with positive charge q.

a. Find the distance x when the rod is horizontal and balanced

b. What value should h have so that the rod exerts no vertical force on a bearing when the rod is horizontal and balanced

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4. Three point charges lie along the x axis. The positive charge q1 = 15.0 C is at x = 2.00 m, the positive charge q2 = 6.00 C is at the origin, and the resultant force acting on negative charge q3 = 9.00 C is zero. What is the x coordinate of q3?

5. Dua buah bola kecil bermuatan sejenis 2μC dan berada pada jarak 20 cm satu sama lain, digantung pada tali sutra ( tidak menghantarkan listrik ) sehingga terbentuk sudut 74o antar kedua tali. Tentukanlah tegangan tali dan massa bola bermuatan tersebut. Risdawati Butarbutar, ST - SMAN2 Soposurung Balige

THE ELECTRIC FIELD11

electric field is said to exist in the region of space around a charged object.

Electric field lines extend – dihasilkan away from positive charge ( where they originate - berasal ) and toward negative ( where they terminate - berakhir )


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the electric field E at a point in space is defined as the electric force Fe acting on a positive test charge q0 placed at that point divided by the magnitude of the test charge:

or

At any point P, the total electric field due to a group of charges equals the vector sum of the electric fields of the individual charges.

o

e

q

FE

2r

QkE

...21 EEE


Example :1. A charge q1 =7.0 C is

located at the origin, and a second charge q2 = 5.0 C 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.

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2. Sebuah partikel bermuatan 5μC dan bermassa 1 mg terapung bebas dalam medan listrik yang ditimbulkan oleh dua pelat bermuatan, seperti terlihat pada gambar. Tentukanlah kuat medan listrik yang mempengaruhi partikel tersebut.

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3. Pada titik-titik sudut B dan D sebuah persegi ABCD masing-masing diletakkan sebuah partikel bermuatan +q. Agar kuat medan listrik di titik A nol, maka di titik C harus diletakkan sebuah partikel bermuatan sebesar ……

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Letak titik P yang kuat medan listrik nol jika berada di sekitar dua benda bermuatan dapat diketahui dengan ketentuan : Jika muatan sejenis titik P

pasti berada diantara kedua muatan

Jika muatan berbeda titik P pasti di luar kedua muatan dan dekat muatan terkecil.

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TIPS :


ELECTRIC FLUX

•Is the product of the magnitude of the electric field E and surface area A perpendicular to the field (ΦE ) ΦE = EA ( ΦE : Nm2/C )

•Electric flux is proportional to the number of electric field lines penetrating some surface.

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Example :What is the electric flux through a sphere that has a radius of 1.00 m and carries a charge of +1.00 μC at its center?


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•If the surface under consideration is not perpendicular to the field

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•The electric flux equation : ΦE = EA’ ΦE = EA cosθ


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1) θ < 90 Φ1 = EA cosθ ( positive)2) θ = 90 Φ2 = 03) 180 > θ > 90 Φ3= EA cosθ ( negative )Risdawati Butarbutar, ST - SMAN2 Soposurung Balige

GAUSS’S LAW

•“The number of electric field lines that penetrate a closed surface is proportional to the amount of electric charge covered by the closed surface”

•Mathematically :

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o

inE

qEA

cos

εo : air ( vacuum ) permittivity ( 8.85 x 10-12 C2/Nm2 )electrical storage ability: the measure of the ability of a nonconducting material to retain electric energy when placed in an electric field.


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A point charge is assume as a sphereSo that,

because

Then,

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o

inqrE

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ko

4

1

2r

qkE in

THE ELECTRIC FIELD DUE TO A POINT CHARGE

THE APPLICATION OF GAUSS’S LAW

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THE ELECTRIC FIELD DUE TO A THIN SPHERICAL SHELL

A thin spherical shell of radius a has a total charge q distributed uniformly over its surface

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The electric field at points inside the shell ( r < a ) zero, because of the spherical symmetry of the charge distribution and because the net charge inside the Gaussian surface is zero

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The electric field at points on the surface the shell we can assume as a point charge with radius a.

The electric field at points outside the shell

oo

in Eq

aE

or 4 2

σ : charge density ( C/m2 )

o

inqrE

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A solid sphere of radius a has a uniform volume charge density ρ and carries a total positive charge q

(a) Determine the magnitude of the electric field at a point outside the sphere.

(b) Find the magnitude of the electric field at a point inside the sphere.

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A Spherically Symmetric Charge Distribution

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A NONCONDUCTING PLANE OF CHARGE

Find the electric field due to a nonconducting, infinite plane of positive charge with uniform surface charge density σ.

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A CYLINDRICALLY SYMMETRIC CHARGE DISTRIBUTION

Find the electric field a distance r from a line of positive charge of infinite length and constant charge per unit length λ.

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Risdawati Butarbutar, ST - SMAN2 Soposurung Balige

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