UCONN Physics 1 & 2 (Scanlon) Chapter 20 Notes: Electric Fields and Forces
A +5.0-μC point charge is placed at the 0 cm mark of a meter stick and a -4.0-μC charge is placed at the 50 cm mark. What is the net electric field at the 30 cm mark? (k = 1/4πε0 = 8.99 × 109 N • m2/C2)
+5 uC (0 cm)____EF(30)___-4 uC(50 cm) E(total) = (9*10⁹)(5*10⁻⁶)/(.3)² + (9*10⁹)(4*10⁻⁶)/(.2)² **add because EF points to the right for both
State the following: - formula for E₁ - formula for E₂
- E₁ = kq₁/d² - E₂ = kq₂/d²
Describe what happens if you scrape electrons onto a cannonball: - location - charge on surface - EF inside conductor
- electrons try to get as far away from each other as possible and spread over the conductor - electrons on surface not inside because they want to be as far away as possible - EF inside cannonball = 0
Describe a hollow metal basketball that has electrons scraped onto it: - electron/proton balance - field lines - EF inside - distribution of charges
- excess electrons on outside - field lines point inward - EF inside = 0; it if wasn't charged it would have more so it was neutral - distribution of negative charges inside to counterbalance
Describe the following charges: - positive - negative
- points away from negative charge - points towards positive charge
Describe the following forces: - attractive - repulsive
- the charges are different - the charges are the same
Describe a capacitor:
- the positively charged left plate has too few electrons - the negatively charged right plate has too many electrons
Consider two point charges located on the x axis: one charge, q1 = 16.5 nC, is located at x1 = -1.667 m; the second charge, q2 = 37 nC, is at the origin (x = 0). What is (Fnet3)x, the x-component of the net force exerted by these two charges on a third charge q3 = -50.5 nC placed between q1 and q2 at x3 = -1.19 m?
-1.667 m (16.5 nC)__-1.19 m (-50.5)__0 m (37 nC) F = (9*10⁹)(-50.5*10⁻⁹)(37*10⁻⁹)/(1.19 m)² F = (9*10⁹)(16.5*10⁻⁹)(50.5*10⁻⁹)/(0.477 m)² then find F(NET)x
What happens to force with Coulomb's Law if you: - double the distance - triple the distance - halve the distance
. F/4 . F/9 . 4F
What do you need for force under Coulomb's Law?
. amount . direction
What is E(F) inside a conductor?
0
What is the fundamental unit of charge?
1.6*10⁻¹⁹ Coulombs; positive for a proton, negative for an electron
What is E₀, the permittivity constant, roughly equal to?
8.85*10⁻¹² C²/Nm²
Two tiny particles having charges of +5.00 μC and +7.00 μC are placed along the x-axis. The +5.00-µC particle is at x = 0.00 cm, and the other particle is at x = 100.00 cm. Where on the x-axis must a third charged particle be placed so that it does not experience any net electrostatic force due to the other two particles?
Closer to weaker particle on the other side of the midpoint at 50 cm It must be placed where the electric fields cancel: k(5 µC)/d² = k(7 µC)/(1-d)² d = 45.8 cm
What are the units for charge?
Coulombs (C)
What is the formula for EF(constant) on a capacitor?
E(constant) = Q/E₀A Q = charge on one plate A = area of one plate = l*w or πr² E₀ = constant: 1/4πk
Describe charges inside a capacitor
EF tangent lines cancel so lines are only perpendicular to the plates
What is another formula for EF(constant)?
EF(constant) = σ/E₀ because σ = Q/A
There are two positively charged particles 5m apart. One has a charge of 8 µC and the other has a charge of 3µC. What is the force between the two particles?
F = kq₁q₂/r² = (9*10⁹ Nm²/C²)(8*10⁻⁶ C)(3*10⁻⁶ C)/(5 m)² the two charges repel
As shown in the figure, three small charges are equally spaced on the arc of a circle that is centered at the charge Q, where Q = +23 nC and all the other quantities are accurate to two significant figures. There are two charges at a 45° angle and 5 cm from the vertical/+23 nC with charges of 2 nC, and a charge between them at no angle from the vertical at -6 nC. What is the magnitude of the net electric force on the charge Q due to the other three charges? (k = 1/4πε0 = 9.0 × 109 N • m2/C2)
The 2 nC charges repel so the vectors are in the opposite direction and the -6 nC charge attracts so the vector points straight up (think an isosceles triangle split down the middle with a line going straight out of the top of it). The base is bisected by these two lines, which cancel because they're opposite. F(2 nC) = kq1q2/r² = (9*10⁹)(2*10⁻⁹)(23*10⁻⁹)/(.05)² * cos 45° * 2(both components) = downward force component upward force component = (6*10⁹)(2*10⁻⁹)(23*10⁻⁹)/(.05)² upward - downward = 2.6 × 10-4 N
A charge of +1.0 nC is 5 cm above the vertical, and a charge of -1.0 nC is 5 cm below the vertical. A dot is 5 cm horizontally from the origin. a) What is the strength of the electric field at the position indicated by the dot? b) What is the direction of the electric field at the position indicated by the dot in the figure? Specify the direction as an angle above the horizontal line.
Using the Pythagorean Theorem, the dot is .05√2 m away from each charge. E = kQ/r² the two sides are the same length of each triangle so Ey = Ex cos 45° E = 2500 N/C at 270° if we assume +x = 0°, +y = 90°, -x = 180°, and -y = 270°
conductor
a material that allows the charge to move
insulator
a material that impedes the movement of charge
What can excess charge outside produce?
a net field
What can a point be and what should test points be for electric fields?
a point can be a positive or negative charge and a test point should be a positive charge of an insignificant amount
What should you have?
a positive and negative charge so the next charge = 0
What is an electric field?
a zone of influence
Indicate where the net electric charge would be for the following situations: a) +q and +q b) +q and +2q c) +q and -q d) +q and -2q
a) equal charges so the midpoint (not accelerating so no EF, only in the middle) b) closer to +q than +2q because +2q has a greater force c) midpoint d) outside of +q pointing left; must be closer to smaller charge and pointing away
Given the two particles q1 and q2, each of which is positively charged, with distance d between them, what is the force of the electric field on q1? What is the force of the electric field on q2?
a) force on q1: F = E₁q₂ force on q1 = electric field on q1 * q2 b) force on q2: F = E₂q₁
Where is EF steady in a capacitor?
all places in the capacitor
Where are lines the most dense?
around charges and near the center between two charges than positive or negative charges because they exist at some point in space
When is the electric field of a test charge weaker?
as it heads away from the charge
What is direction for force?
attraction (different charges) or repulsion (like charges)
What is the formula for charge?
charge = nq ex. 8*10⁻⁶ C = n(1.6*10⁻¹⁹) n = # of electrons missing = 5*10¹³ electrons
What is a key property of conductors?
charges are free to move around inside in response to internal electric fields; in a static situation, they will arrange so that the internal field is zero.
What should you do if given multiple charges>
concentrate on 2 charges
What is EF on a capacitor?
constant
Coulomb's Law
describes the force the charges exert on each other F = kq₁q₂/r² k = constant q1 = charge 1 q2 = charge 2 r = distance between them
What should you indicate for an electric field?
direction and strength
How can you find force using vectors between the points of an equilateral triangle that are two positive charges and one negative charge?
draw vectors based on the direction EF lines would point in relation to the two other sides; some are positive and some are negative so find the sums F² = Fx² + Fy²
Describe charges on the surface of a conductor
electric field lines approach each electron from several angles and they cancel out so EF is perpendicular to the surface
Describe electric fields with negative charges
electric fields with negative charges have positive charges pointing radially inwards towards the particle
Describe electric fields with positive charges
electric fields with positive charges have positive charges pointing radially away from the particle
What happens if the two plates in a capacitor are briefly connected?
electrons fly off the negative plate and neutralize both
What can you do with enough positive test charges?
figure out the pattern
What happens to electric field on a capacitor?
it always flows from the positive plate to the negative plate **lines are straight between the two plates and curve outside of them
What is the constant k?
k = 9.0 * 10⁹ Nm²/C²
What should you equate charge to?
mass (scalar)
What do electric field lines do?
move away from positive charges and towards negative charges; check using a positive test charge
Where does charge flow?
neutrality is more common than positive or negative charges and charge flows to neutrality
Can electric field lines cross?
no **why it must be tangent to EF lines
Describe the electric field between two of the same charges
place a test point between them; there is 0 electric field in the middle between them because the two forces are the asme and cancel εE(F) = 0
What are the two types of charges?
positive and negative
What happens if a force = qE?
the charge accelerates; F = qE = ma
What happens if you have a charged ball and an uncharged ball and you touch them together then separate them?
the charges are Q and neutral; electrons then spread equally so after the charges are Q/2 and Q/2
How do you describe the direction of an electric field?
the direction of an electric field is the direction a positive charge would go
What happens if electrons are scraped onto an insulator?
the electrons will stay on that area and not move
if you are given the following from left to right: negative charge, negative charge, positive charge how do you find the direction?
the first charge has a larger vector in the opposite direction due to its interaction with the second charge, and a smaller vector pointing towards the third charge to the right. Therefore, the next direction is to the left
Describe an electrically neutral substance?
the number of electrons = the number of protons
What happens if you have several conductors next to each other in a line and they slowly get smaller so they make a line? What happnes if a person is next to them?
the smallest becomes a point charge, and the person at the end has an electric field pointing towards it. E = kq/d² where d = total distance (radius + distance between)
Describe electric field lines given a positive particle and a negative particle
the two are connected by electric field lines, which flow towards the negative charge and away from the positive charge; test charges do the same and rest on a tangent to the electric field lines
Describe conservation of charge
there is a static amount of charge in the universe and it cannot be transformed
Describe valence electrons in a conductor
they are loosely held and free to move in the conductor; they will respond until EF = 0 or continute to accelerate until they rearrange to make it 0
Describe electric field vectors
they are tangent to the direction of electric field lines at any given point
What do the two forces of the electric field on q1 and q2 equal?
they are the same; Fq₁ = Fq₂
Describe negative charges
they have more electrons than protons
Describe positive charges
they have more protons than electrons
Describe insulators
they impede the spread of charge and their insides will NOT be 0
A positively charged particle of 5 µC and a negatively charged particle of -2 µC are 6 meters apart. What force do they exert on each other?
two opposite charges = attraction; forces exerted on each other so opposite and equal F = kq₁q₂/r² F = (9*10⁹ Nm²/C²)(5*10⁻⁶ C)(2*10⁻⁶ C)/(6)² absolute value of charge F = 0.0025 N
capacitor
two plates with opposite charge
One point charge +Q is placed at the center of a square, and a second point charge -Q is placed at the upper-left corner of the square. It is observed that an electrostatic force of magnitude 2.0 N acts on the positive charge at the center. Now a third charge -Q is placed at the lower-left corner of the square, as shown in the figure. What is the magnitude of the net force that acts on the center charge now?
two right triangles each with a hypotenuse of 2 N. Find the y components of both and add them = 2.8 N
How can you find the magnitude and direction of the electric field at each location?
use the vector sum of the electric field vectors for each individual charge ex. a charge will move away from one particle in one direction (at a certain angle) and towards another in another direction at a different angle. you can use this to create a right triangle
What are electric fields?
vectors
When is a field stronger?
when there are more field lines AND closer to the particle
What can you create according to conservation of charge?
you can't create electrons but can create electrons and antielectrons
What is the formula for charge density (σ)?
σ = Q/A
