What Potential Difference Is Required to Bring the Proton to Rest?
Due: Monday, February sixteen, 2015 at 12:xxx PM PST
Covered concepts: Electric potential, electric potential energy, capacitance
Chapter 20: Electric Potential and Electrical Potential Energy
Note:I decided to change the format a petty. And again, do non only jump directly to the reply, that volition Non help you pass exams fifty-fifty with open up notes. Be sure to ask any questions you have in the comment section and I will endeavour to reply them every bit apace as possible.
Note 2:U = potential free energy (PE). I utilize these notations interchangeably.
Looking for a specific problem? Attempt ctrl+f (⌘+f on macs) and searching for a snippet of the problem, or scroll down as the problems are listed in society of assignment.
i. Walker 20.9. The Earth has an electrical field with a magnitude of approximately 104 V/grand about its surface. What is the potential difference betwixt a point on the basis and a indicate on pinnacle the Washington Monument (555 ft high)?
Equation:
|ΔV| = EΔd
Given Values:Listen your units! Nosotros want to convert any non-SI into SI units!
East = 104 Five/m
d = 555 ft
Hint 1:This is a pretty straight forward question. Potential difference is the product of the electric field and distance between the ground and the point at the tiptop of the monument.
Hint 2:Are y'all using the right units? There are 0.305 meters in i foot.
Answer:
|ΔV| = (104 V/m)(555 ft)(0.305 thou/ft) = 17604.half-dozen V
I'm nonetheless getting the wrong answer!
1. Check your calculations and units! This is the well-nigh common reason for me to become a wrong answer.
two. Walker 20.14. Living cells actively "pump" positive sodium ions (Na+) from within the cell to exterior the cell. This process is referred to as pumping because piece of work must be washed on the ions to move them from the negatively charged inner surface of the membrane to the positively charged outer surface. Assume that the electric potential is 0.080 V higher outside the jail cell than inside the cell, and that the prison cell membrane is 0.12 µm thick. (It is estimated that as much equally 20% of the free energy we consume in a resting country is used in operating this "sodium pump.")
(a) Calculate the work that must be done to move ane sodium ion from within the cell to exterior.
(b) If the thickness of the cell membrane is increased, does your answer to role (a) increase, decrease, or stay the aforementioned? Explain.
Equation:
W = CΔV
Given Values:Mind your units! We want to convert whatsoever non-SI into SI units!
ΔV = 0.080 V
d = 0.12 µm
qNa+ = i.6 ten 10-nineteen C (This is because a sodium ion has a positive charge — i.e., one less electron — so information technology has the charge of +east. You should memorize the charge of e.)
Hint 1:Again a very straightforward question but at that place are tricky! They give yous a value that yous don't actually need to utilize to confuse you.
Reply:
ΔU = W = CΔV = (1.6 x 10-19 C)(0.080 Five) = 1.28 x 10-20 J
As yous can see, distance does not matter in the calculation of work then whether the thickness of the membrane is increased or decreased has no impact on the answer to function (a).
I'm still getting the wrong answer!
1. Check your calculations and units! This is the most mutual reason for me to become a wrong answer.
three.Walker xx.22. A proton has an initial speed of four.1 
x5 m/due south.
(a) What potential difference is required to bring the proton to balance?
(b) What potential difference is required to reduce the initial speed of the proton by a gene of 3?
(c) What potential difference is required to reduce the initial kinetic energy of the proton by a factor of 3?
Equation:
KE+ PE = Constant
Given Values:Listen your units! Nosotros want to catechumen any not-SI into SI units!
fivei =4.1 10five g/due south
vf = 0 m/s
grandproton = i.67 10 x-27 kg
qproton = 1.threescore x 10-19 C
Hint 1: Call up the equations for kinetic energy and potential energy from PHYS 114? Using them, it's a simple plug and chug.
Hint two: At residue, the initial and terminal (KE + PE) are equal.
(a) Respond:
(KE + PE)i = (KE + PE)f
and 
so:
To make calculations easier, rearrange to:
Plug and solve for ΔV = vf – 5i = 877.27 V = 0.88 kV.
(b) Answer:
If you plug in (1/iii)fivei for vf instead of 0 and solve for ΔV, you become ΔV = 779.viii 5 = 0.78 kV.
(c) Reply:
If you plug in (one/3)KEi for KEf and solve for ΔV, you get ΔV = 584.85 V = 0.58 kV.
I'thou still getting the wrong answer!
1. Cheque your calculations and units! This is the near mutual reason for me to get a wrong answer.
4. Walker twenty.29. How far must the point charges q 1 = +vii.22 µC and q 2 = – 29.5 µC be separated for the electric potential energy of the organisation to exist – 145 J?
Equation:
Given Values:Heed your units! We desire to convert any non-SI into SI units!
Coloumb's consant thousand = eight.987 10 109 Northward•m² / C²
qane = 7.22 µC = 7.22 x 10-6 C
qii = -29.5 µC = -29.five x ten-6 C
PE = -145 J
Hint 1: I love uncomplicated plug-and-chug questions 😀
Hint two: Make sure you lot are using the right units and signs!
Answer:
Plug in values and solve for r = 0.013 grand = 1.32 cm.
I'm yet getting the wrong respond!
1. Check your calculations and units! This is the most mutual reason for me to get a incorrect answer.
five.Walker 20.33. A dipole is formed by point charges + iii.1 µC and -three.1 µC placed on the x-axis at (0.xx m, 0) and (-0.20 m, 0) , respectively.
(a) Sketch the electric potential on the x axis for this organization.
(b) At what positions on the x-axis does the potential accept the value vi.two ten5 V?
Equation:
Given Values: Mind your units! Nosotros desire to convert any not-SI into SI units!
Coloumb'south consant k = 8.987 x 109 Northward•m² / C²
qone = iii.1 µC = 3.ane x ten-6 C
q2 = -iii.one µC = -iii.ane x 10-6 C
V = 6.ii 105 5
r = 0.20 yard
(a) Hint 1: Electric potential on point charges go asymptotic.
(b) Hint 2:Information technology'due south a simple plug and chug, though you do have to practice information technology twice.
Hint 3:Are y'all using the correct signs? Remember one is positive and ane is negative.
(a) Reply:
Click to enlarge
(b) Answer:
For the left hand position, solve the get-go equation with qaneand r = 0.20 1000 to get x = 0.sixteen m.
For the right hand position, solve the second equation with q2and r = -0.xx thousand to go ten = 0.24 grand.
I'thousand still getting the wrong answer!
one. Cheque your calculations and units! This is the most common reason for me to become a wrong respond.
ii. Brand sure you are using the correct signs also. The calculation for this trouble can get tricky, so practice them in manageable parts if that helps.
6.Walker 20.37. The figure beneath shows three charges at the corners of a rectangle of length x = 0.xv m and superlative y = 0.10 m.
(a) How much work must exist done to move the +ii.vii-µC charge to infinity?
(b) Suppose, instead, that we motion the −half dozen.1-µC charge to infinity. Is the work required in this case greater than, less than, or the same as when we moved the +2.7-µC charge to infinity? Explain.
(c) Summate the piece of work needed to move the -6.1-µC charge to infinity?
Equation:
ΔU = Uf – Ui
Given Values: Heed your units! We want to catechumen any non-SI into SI units!
Coloumb'southward consant g = 8.987 x xix North•thou² / C²
q1 = -half dozen.i µC = -6.1 x 10-half dozen C
q2 = 2.vii µC = 2.7 x 10-6 C
qthree = -3.3 µC = -3.3 10 x-6 C
10 = 0.fifteen m
y = 0.10 thou
Hint 1: Y'all have three points and two distances between them, and you are looking for the work needed to movement ane of the charges. So how do y'all need to put together the needed equation?
Hint 2: What happens to the final electric potential if you move a point charge abroad past a altitude of infinity?
(a) Respond:
Plug in and solve for West = 1.43 J.
(b) Answer:
In part (a), we were trying to take a positive charge away from a negative charge. As yous know, opposite charges attract so this will accept an actress effort (positive work). However, if we try to take away a negative charge from a negative accuse we actually get a negative piece of work as they repel each other. Therefore, the work required in this example is less than what we got in office (a).
(c) Respond:
Modify the equation from part (a) to stand for to moving the other charge:
Plug in and solve for W = -0.82 J.
I'm still getting the incorrect respond!
one. Check your calculations and units! This is the most common reason for me to get a wrong answer.
two. Final electric potential is zero when y'all move a indicate charge away by a distance of infinity.
3. Are you using the right r23 value? qtwo and q3 are located diagonally from each other so yous need to use Pythagorean'due south Theorem to find the correct altitude.
7.Walker xx.55. A parallel-plate capacitor has plates with an area of 0.025 one thousandii and a separation of 0.77 mm. The space betwixt the plates is filled with a dielectric whose dielectric abiding is 2.0.
(a) What is the potential difference between the plates when the charge on the capacitor plates is 4.7 µC?
(b) Volition your answer to part (a) increment, decrease, or stay the same if the dielectric constant is increased? Explain.
Equation:
Given Values: Mind your units! Nosotros want to convert whatsoever not-SI into SI units!
A = 0.025 mii
d = 0.77 mm = 7.7 x x-iv m
Q = 4.7 µC = four.7 10 10-6 C
Dielectric constant κ = 2.0
Vacuum permittivity ε0 = 8.85 x 10-12 C2/N•chiliad2
Hint 1:This is some other simple plug and chug question.
(a) Reply:
Plug in values and solve for Five = 8178.53 5 = 8.18 kV.
(b) Answer:
Because nosotros are dividing by the dielectric constant, if everything else stays the same, increasing κ will decrease V.
(c) Answer:
Calculate the same equation with κ = 4.6, for 5 = 3555.88 Five = 3.56 kV.
I'm still getting the incorrect answer!
1. Check your calculations and units! This is the most common reason for me to go a wrong answer.
8.Walker 20.57. A parallel-plate capacitor with plates of area 2.75 10-4 m2. What plate separation is required if the capacitance is to be 1330 pF, when the space between the plates is filled with each of the following?
(a) Air
(b) Glass
Equation:
Given Values: Mind your units! We want to catechumen any not-SI into SI units!
A = ii.75 10-4 mtwo
C = 1330 pF = 1330 ten 10-12 F
Vacuum permittivity ε0 = 8.85 ten 10-12 C2/N•mii
Dielectric constant κair = 1.0
Dielectric constant κglass = v.half dozen
Hint one:This problem is like to the previous question, you just have to solve for a different variable (d).
Hint 2:But nosotros're not given Q??? Don't worry, endeavor solving the equation for d. You lot'll see that Q cancels out.
Answer:
Plug and solve for dair = i.83 x ten-half dozen one thousand and dglass =ane.02 10 10-5 one thousand.
I'm still getting the wrong reply!
1. Cheque your calculations and units! This is the most common reason for me to get a wrong answer.
two. Make certain yous are using the right dielectric constant. 5.6 for glass is the value given by the textbook, however Googling information technology will give you various dissimilar values, such as 4.7 or 3.8.
9.Walker 20.threescore. (a) What plate surface area is required if an air-filled, parallel-plate capacitor with a plate separation of ii.9 mm is to have a capacitance of 25 pF?
(b) What is the maximum voltage that tin exist applied to this capacitor without causing dielectric breakdown?
Equation:
5max = Emaxd
Given Values: Mind your units! We want to catechumen whatever non-SI into SI units!
d = two.nine mm = 0.0029 thousand
C = 25 pF = 25 10 10-12 F
Vacuum permittivity ε0 = 8.85 10 ten-12 C2/Due north•mtwo
Dielectric constant κair = 1.0
Dielectric strength Eair = 3.0 10 106 V/m
(a) Hint i: Apply the same equation as the previous two problems, solving for a different variable (A).
Hint 2:But nosotros're not given Q??? Don't worry, attempt solving the equation for d. You'll see that Q cancels out.
(b) Hint 3: It's a simple plug and chug.
(a) Answer:
Plug in values and solve for A = 0.0082 thousand2 .
(b) Answer:
Plug in values and solve for Vmax = 8700 V = 8.7 kV.
I'yard withal getting the wrong answer!
ane. Check your calculations and units! This is the most common reason for me to get a wrong answer.
10.Walker 20.65. The membrane of a living cell tin exist approximated by a parallel-plate capacitor with plates of area 5.47 10-9 mii, a plate separation of 8.5 ✕ 10−9 grand, and a dielectric with a dielectric abiding of 4.five.
(a) What is the free energy stored in such a cell membrane if the potential difference across it is 0.0835 Five?
(b) Would your answer to office (a) increase, decrease, or stay the same if the thickness of the jail cell membrane is decreased? Explain.
Equation:
Given Values: Heed your units! We want to convert any non-SI into SI units!
A = 5.47 10-9 m2
d = viii.5 ✕ 10−9 grand
ΔV = 0.0835 V
Vacuum permittivity ε0 = 8.85 x 10-12 C2/N•10002
κ = iv.5
Hint ane: Another uncomplicated plug and chug. Boy, this homework is easy (:
(a) Respond:
Plug in values and solve for U = eight.93 x 10-xiv J.
(b) Answer:
Looking at the equation, you can see that d is in the denominator, which means as d decreases, U volition increase.
I'm still getting the wrong reply!
one. Check your calculations and units! This is the most common reason for me to get a wrong answer.
11.Walker xx.69. An electronic wink unit of measurement for a camera contains a capacitor with a capacitance of 840 µF. When the unit is fully charged and gear up for operation the potential difference betwixt the capacitor plates is 310 V.
(a) What is the magnitude of the accuse on each plate of the fully charged capacitor?
(b) Find the free energy stored in the "charged-up" flash unit.
Equation:
and 
Given Values: Heed your units! We desire to convert any non-SI into SI units!
C = 840 μF = 840 x 10-6 F
ΔV = 310 5
Hint 1: Some other simple plug and chug, for both parts.
(a) Answer:
Plug in values and solve for Q = 0.26 C.
(b) Answer:
Plug in values and solve for U = 40.36 J.
I'm still getting the wrong respond!
ane. Check your calculations and units! This is the most common reason for me to go a wrong answer.
Source: https://uwphysics115helper.wordpress.com/2015/02/14/problem-set-6/
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