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PHYS 212- Spring 2014
Exam #1- Review Sheet
General tip
Becarefulaboutunits inElectromagnetism. Oftenprefixesareusedasthere aresmallorlargequantities.
Always convert prefixes back to the base unit before using them mathematically. Sometimes you can find
the correct choice by checking the signs/dimensions/limiting behavior.
Vectors
Vectors are shown by arrows. The length of arrow is proportional to the magnitude of vector. Vectors can be
projected into their components
๐ฆ
๐ด ๐ฅ ๐ดcos๐ ๐ดโ
๐ด = ๐ดsin๐
๐ฆ
๐
๐ฅ
Add vectors component by component:
๐ถ = ๐ด + ๐ตโโ โ ๐ถ = ๐ฅ + ๐ต๐ฅ ๐ฅ ๐๐๐ ๐ถ๐ฆ= ๐ด +๐ฆ๐ต ๐ฆ
Coulombโs Law
The electric force between two point charg1s ๐ and2๐ is given by
๐ ๐ ๐ 1 ๐๐ 2
๐น = 1 2 ๐12 ๐คโ๐๐๐ ๐ = = 9 ร 10 9
๐12 4๐๐ 0 ๐ถ2
Note that this has a similar form to the gravitation force between two masses, however, it can be either repulsive or
attractive (like charges repel, unlike charges attract each other).
Use superposition principle to compute the net force on charge q due1to 2 , ๐ , โฆ.
๐ 1 ๐น3
๐1 ๐น2
โ2 ๐2
๐ โ
๐
๐น1
๐ โ3
3
๐ ๐1๐ ๐ ๐ 2 ๐ ๐ 3
๐น ๐ก ๐น +1๐น + 2 = โ3 2 ๐1 + 2 ๐2 + 2 ๐3
๐1 ๐2 ๐3
Be careful here, you are adding vectors!
Electric Field
The electric field summarizes the influence of a collection of charges on any โtest chargeโ q that we place in their
vicinity.
โ
๐ธ = ๐น
๐
And for the example above it is going to be
๐ ๐ 1 ๐ ๐2 ๐ ๐3
๐ธ = ๐ธ +1๐ธ + 2 = โ3 2 1ฬ + 2 ๐2 + 2 ๐3
๐1 2 3
Questions & Corrections: Hassan Shapourian ([email protected]) PHYS 212- Spring 2014
Exam #1- Review Sheet
Notice that electric field is a property that we assign to the space surrounding a collection of charges. So, it doesnโt
โโ
depend on the test charge. Electric field is a vector field denotedโ); i.e. it has magnitude and direction at every
point of the space.
Electric field lines: a graphical representation of ๐ธโ) following these rules
๏ท Field lines originate from positive charges and end on negative charges
๏ท Field lines are continuous and never cross (except at the position of point charges)
๏ท The number of field lines connected to a charge is proportional to that chargeโs magnitude.
Important result of field lines representation:
The electric field is stronger where the field lines are denser.
Note that what matters is the density of field lines, being on a field line itself doesnโt imply a stronger field!
Mechanical Equilibrium
A system is said to be in equilbirum where the net forcce on it vanishes. There are three types of equilibria:
๏ท Stable equilibrium: in this situation, once the system is slightly disturbed from equilibrium point, it
experiences a restoring force and meets the equilibrium point periodically. Generally, this case can be
demonstrated by a potential energy and force as in
๐(๐ฅ) ๐น(๐ฅ)
๐ฅ
๐ฅ
๏ท Unstable equilibrium: here, if the system is disturbed, it moves away from the equilibrium point. Not
only is there no restoring force, but also the force tends to push the particle away.
๐(๐ฅ) ๐น(๐ฅ)
๐ฅ
๐ฅ
๏ท Indifferent equilibrium: the system is indifferent to any perturbation.
๐(๐ฅ)
๐ฅ
The fastest way to determine the type of equilibrium is to displace the particle from it equilibirum position and find
the dominant force.
Gaussโ Law
Electric flux: the total field strength passing through a given surface. In a fluidic system, it would be net amount
of fluid passing through a surface per unit time.
ฮฆ = โซ๐ธ.๐๐ด = โซ๐ธ cos๐ ๐๐ด
Questions & Corrections: Hassan Shapourian ([email protected]) PHYS 212- Spring 2014
Exam #1- Review Sheet
where ๐๐ด is directed normal to the element of area ๐๐ด with magnitude equal to area of that element. In
case of uniform field on flat surface, it is simplified into ฮฆ = ๐ธ๐ดcos๐.
Statement of Gaussโ law: the total electric flux through any closed surface is propotional to the total
amount of charge enclosed by that surface.
๐ ๐๐๐
ฮฆ = โฎ๐ธ.๐๐ด =โ ๐
0
Note that ๐๐ด is always directed outward for a closed surface.
Application of Gaussโ law: We can use Gaussโ law to compute the electric field for some symmetric chage
distributions. Here is a four-step procedure to do this:
๏ท Sketch the electric field lines using all the symmetries of the problem.
๏ท Choose a suitable Gaussian surface based on the geometry of the problem.
๏ท Determine the total charge enclosed by your surface.
๏ท Evaluate the flux integral and combine it with Gaussโ law to dete๐ธ.ine
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