2 a ZH EM I Coulombs Law E Field Intensity

8/10/2019 2 a ZH EM I Coulombs Law E Field Intensity

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Dr. Zuhair M. Hejaz Set 2 a Coulombs Law & E-Field Intensity 1

Coulombs Law and

E-Filed Intensity

Set 2 a


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Coulomb's Law



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Coulomb's Law Coulomb's law: The force between two

electrical charges and , separated in

vacuum or free space is:

1. Along the line joining them.

2. Directly proportional to the product of the

charges.

3. Inversely proportional to the square of the

distance between them.

Mathematically



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Coulomb's Law

is proportionality constant

is The constant known as thepermittivity

of free space and has the value

In SI units, charges and are measuredin Coulombs (C), the distance is in meters

(m), and the force is in Newtons (N).



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Coulomb's Law Note that 1 C is approximately equivalent to

electrons. It is a very large unit of

charge because one electron charge is:

Coulomb's law is now

If point charges and are located at

points having position vectors and as

shown in the fig. to follow Dr. Zuhair M. Hejaz Set 2 a Coulombs Law & E-Field Intensity 5


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Coulomb's Law

then the force on caused by

is given by: Vector form

where ; and Dr. Zuhair M. Hejaz Set 2 a Coulombs Law & E-Field Intensity 6

F1


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Coulomb's Law

Example 1: A charge is located atpoint and a charge is

located at point in a vacuum, find the

force exerted on . Solution:



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Coulomb's Law- Example 1

check!

The unit vector is then:

Thus, the force is found using:



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Electric FieldIntensity



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Electric Field Intensity The Electric Field Intensity (or electric field

strength) is the vector force on a unitpositive test charge when placed in the

electric field.

The force exerted on the test charge isexpressed as:

As a force per unit test charge, the eqn.becomes:



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Electric Field Intensity The term on the right and the directed line

from to the position of test charge

describe a vector force called Electric Field

Intensity and expressed as:

so,

and measured by Volts per meter (V/m) .

Note that: the last eqn. is the Electric Field

Intensity caused by a single point charge



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Electric Field Intensity For a point charge located at the origin of a

Cartesian coordinates:

We have:

;

and

So,

This shows the field complexity in 3D coordinates.



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Electric Field Intensity

Now, consider a point charge, not located at the

origin of our system, but at , so

We find the electric field

intensity at point due to

the point charge, where

Expressing , we finally find the field



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Electric Field Intensity

Now for 2 point charges

the electric field intensity on test charge is

obtained as the sum:

Recall that Coulomb forces are linear.Dr. Zuhair M. Hejaz Set 2 a Coulombs Law & E-Field Intensity 15


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Electric Field Intensity-Example 2

Example 2:

Find the

Electric

FieldIntensity

at point

P(1,1,1) caused by the 4 identical charges locatedat P1(1,1,0), P2(-1,1,0), P3(-1,-1,0) and P4(1,-1,0)

(each has 3 nC charge). Solution



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Electric Field Intensity-Example 2

Solution:

r at P(1,1,1): and

Then and the magnitudes are:

Using the expression for the field , we find

As , we find the term:



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Electric Field Intensity-Example 2 Recall the unit vectors:

;

Now substitute the other terms in:

Simplify to



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Electric Field Intensity Note that if the field intensity is required NOT

just at a point without charge, BUT on anotherpoint charge having a charge, then the eqn.:

Becomes:



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Practice Exercise

Problem:

Point charges with (1 mC) and (-2 mC) are

located at P1(3, 2, -1 ) and P2(-1, -1, 4),

respectively. Calculate the electric force on a

(10 nC) charge located at P(0, 3, 1) and theelectric field intensity at that point.

Answers:

At the point P(0, 3, 1)



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You have learned about

Coulomb's law for the force between two

static point charges.

The vector force of electric field intensity

caused by 1, 2 and n point charges at a point.

The vector force of electric field intensitycaused by n point charges on another point

charge.



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End of Set 2 a

Thank You for YourAttention


2 a ZH EM I Coulombs Law E Field Intensity

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