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phys 5c midterm 1 study guide

Terms in this set (40)

hookes law
Hooke's law: F=kx, linear expansion of taylor series where drop irrelevant term, rewrite 1st term and do an approx
reductionist
reduce, lil detail
vector
length and direction! v>=vxx^+vyy^+vzz^
scalar
a number, no direction
newtons second law
Force=ma, where m is scalar and a is vector
superposition
Superposition: v=v1+v2, use arrow tail method. Each component (x,y,z) also it
taylor series
Taylor series: f(x)=f(x0)+f'(x0)(x-x0) + ½ f''(x0)(x-x0)2...
Like a particle in a well at eq, how move around when there's a force? In a spring, use linear approx: F(x)=f'(0)x, and thus F(x)=-kx in linear harmonic oscillation
charges: expand arbitrary charge until we see a pt
Then one charge, all i see from far away is net charge
Zoom→ dipole, no rlly help unless first term is 0, so k=0 and 2nd order is imp
And then closer we see diff charge distribution
elect charge units of:
proton + e- , coulomb, +/+ repel, +/- attract. E, field spin
charge is conserved
can be distributed diff
conductor and insulator
Some materials conduct, like metal and lightning. rubber=insulator aka dielectric
conductor
In these, charges can freely move!
An E field make F that push charge to flow in 1 dir
insulator
Charge no free move, only lil bit. Still react, like polymerization! No free charge
induction of dipole how
Induction of dipole by put slab in e field=polarization. Now e field inside dielectric is diff than e field outside
when net F=0
→ eq
Spring PE: stable at bottom of U, when slope is 0 in pot its an extrema. Like a pendulum, upside down U is PE and unstable at max extrema; a movement it falls off
coulomb's law
F=kq1q2/r2
If x2 as much charge, then Fx2. its proportional! Stronger charge need more repel, closer it is, the stronger so 1/r. r2 bc gravity
F always b/w 2 particle that connect it
forces of charges
← + + → + → ← -
If they're both negative, the force is away (the direction of 1 on 2 and then the negative charge is positive, so same dire). If opp charge, F is toward (dir 1 on 2, and then the opp charge turn it the other dir)
unit vectors
r^=r>/||r>||
r^ is a vector! Can add vector, not scalar. +/- depending on coord sys. No unit
field model general def
In the field model, A alter space around it (field) and alteration of space (electric field) is agent that exert a F on B
field model more indepth
1) a group of source charges alter the space by creating an elect field
2) if another charge q is place in field, exper F exerted by field . E>=F>/q
Magnitude E of elect field is called elect field strength
Elect field is the agent that exert an elect F on a particle w/ charge q
1) elect field, a vector, exists at every pt in space
2) if probe charge q is positive, the elect field vector pt in the same dir as the F on the charge; if neg, field vector pt opp the F
3) elect field is independent of charge q that probes field; depend only on source charge
elect field rules
1) elect field, a vector, exists at every pt in space
2) if probe charge q is positive, the elect field vector pt in the same dir as the F on the charge; if neg, field vector pt opp the F
3) elect field is independent of charge q that probes field; depend only on source charge
elect field of a pt charge
Elect field of pt charge q at dist r from charge: E>=k|q|/r2 ← away if +q, toward if -q
Coulomb's law describe F b/w 2 charge, elect field is field of single charge
can b written in terms of permittivity const:
ε0= 1/4πk=8.85E-12 [C2/Nm2]
E=1/4πε0• |q|/r2 ← away if +q, toward if -q
elect field diagram: show representative elec field vector
If charge +, all vector pt away from it. If negative, all vector pt toward it
Arrow indicate dir and strength of field at pt to which tail of vector placed
Each vector represent the ele field at one pt in space
elect field of multi charge
Net elect field from group of pt charge: E>net=F>on q/q=F>1 on q/q+F>2 on q/q=E>1+E>2=∑E>i
Net E field is vector sum of E field due to each charge; principle of superposition
elect field of a dipole
In permanent elect dipole, the opp charge particle maintain a small permanent separtoin
We can also creat elect dipole by polarizing a neutral atom w/ an external field. This is induced elect dipole!
We can represent an elect dipole by 2 opp charges +/- q separated by a small dist s
For a pt on the axis of dipole, it/ll b a dist y-s/2 from positive charge and y+s/w from the negative charge
E=1/4πε0 •q• (1/(y-½ )2-1/(1- +y-½ yes)
Edipole: =1/4πε0•2qs/y3
how to make an elect dipole
In permanent elect dipole, the opp charge particle maintain a small permanent separtoin
We can also creat elect dipole by polarizing a neutral atom w/ an external field. This is induced elect dipole!
We can represent an elect dipole by 2 opp charges +/- q separated by a small dist s
For a pt on the axis of dipole, it/ll b a dist y-s/2 from positive charge and y+s/w from the negative charge
to visualize an E field
draw elect field line:
E field line r continuous curves tangent to the Elec field vector
Closely spaced field lines indicate a greater field strength
Elect field line start on + charge and end on (-)
Elect field line never cross
elec field line draw
Some ex: elec field line of + pt charge, a (-) pt charge, and a dipole
+ away, (-) toward, same
dipole moment
p=qs, pointoing from negative to positive charge. Write elec field on axis of dipole: Edipole: =1/4πε0•2p>/r3.
Elec field in plane that bisect dipole: Edipole: =-1/4πε0•p>/r3
a charged sphere elec field
For a sphere of radius R w/ a total charge Q spread out uniformly throughout it, its elect field when r>R: E>: =1/4πε0•|Q|/r2
Will pt away from sphere if Q is positive, and toward sphere if Q is negative
parallel plate capacitor
Two metal plate (electrode), one w/ charge +Q and one w/ charge -Q, r place face to face a dist d apart. Parallel plate capacitor
Elec field inside a parallel plate capacitor whose plates have area A is: E>=Q/ε0A from positive to negative. Elec field outside the capacitor is zero
Elec field prop to charge; bigger area over which fixed charge distributed influence elect field.
Outside capacitor, E is opp so net field is zero. Inside, E+ and E-r parallel so net field large
elec field and parallel plate capcitor
Elec field inside a parallel plate capacitor whose plates have area A is: E>=Q/ε0A from positive to negative. Elec field outside the capacitor is zero
Elec field prop to charge; bigger area over which fixed charge distributed influence elect field.
Outside capacitor, E is opp so net field is zero. Inside, E+ and E-r parallel so net field large
uniform elec field
one that is same in strength and dir at every pt in a region of space, analogous to uniform gravitational field near the surface of the earth. Easiest way to produce one is within a parallel plate capacitor
elec field around and within conductor
1) elec field is zero at all pt inside a conductor in electrostatic eq
2) any excess charge on the conductor must lie at its surface
3) elec field at the surface of a charged conductor is perpendicular to the surface
motion of charged in an elec field
If Fon q is the only F acting on q, it cause charge particle to acc: a=Fon q/m=q/m E>
Ratio q/m is imp for the dynamics of charged-particle motion, and is called the charge-to-mass ratio
A charged particle in a uniform elec field will move w/ const acc
Elec field exert a F on a charged particle
motion w/ drag
A charged obj that move through a medium exper a drag F, almost always at a low Reynolds number, so that the drag F is D=bv, dir opp the motion, where drag const b depends on the obj size and viscosity of the medium
A charge obj that move through a viscous medium in response to an elect F of magnitude Fapplied=qE will acc until it reach terminal speed: vterm=qE/b
torque on dipole
Bc charges at either end of dipole r equal in magnitude but opp in sign, there is no net F on a dipole in a uniform elect field
however , the elect field does exert a torque on the dipole, rotating it until it is aligned w/ the elect field.
T=2x dF+ =2(½ s sinӨ)qE=pEsinӨ
dipole nonuniform
For any nonuniform elec field, the net F on a dipole is toward the dir of the strongest field.
Bc any finite-sized charged obj has a field strength that inc as u get closer, a dipole will exper a net F toward any charged obj
summary
Coulomb law
F1 on 2=F2 on 1= F b/w 2 charge particle q1 and q2 sep by dist r is where electrostatic const is K=9E9 Nm2/C2
F r interaction pair direct along line join particle
F is attractive two opp charges, repulsive 2+ like charges
Net F on a charge obj vector sum of the F due to all other charges
SI unit of charge is [C]
Equations
equation
Hooke's law: F=kx
v>=vxx^+vyy^+vzz^
Coulomb's law: F=kq1q2/r2 •r^ where F[N], r=dist[m], q=charge [Coulomb aka C]
e- charge: 1.6E-19 C
k=9E9 [Nm2/C2]
k=1/4πε0
ε = permittivity of free space
E>=F>/q
Of pt charge: E>=k|q|/r2 ← away if +q, toward if -q
E=1/4πε0 •|q|/r2 ← away if +q, toward if -q
ε0= 1/4πk=8.85E-12 [C2/Nm2]
elect field of multi charge: E>net=F>on q/q=F>1 on q/q+F>2 on q/q=E>1+E>2=∑E>i
p=qs, Edipole: =1/4πε0•2p>/r3, Edipole: =-1/4πε0•p>/r3
Charge sphere: E>: =1/4πε0•|Q|/r2
Parallel plate capacitor: E>=Q/ε0A
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