Potential and Electric Potential

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physics 112

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The questions in this section are to be answered by circling the correct multiple-choice answer AND providing a short justification of your answer in the space after the problem..

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Name: Lab Day/Time: Monday Homework 5 Potential Multiple Choice Problems The questions in this section are to be answered by circling the correct multiple-choice answer AND providing a short justification of your answer in the space after the problem.. Monday Homework Problem 5.1 Which of the following best describes how a conductor lowers the electric field in its interior? Select One of the Following: (a) Electric field lines cannot penetrate conducting atoms. (b) A conductor does not allow field lines through its surface. (c) The electric field causes a continuous flow of charge which upsets the field. (d) A surface charge is set up that creates an electric field which cancels the applied field. Monday Homework Problem 5.2 A dielectric slab is placed in a external field as shown to the right. Outside the slab, the electric ~ 0 = (10.0N/C)x̂. Inside the slab, the electric field is field is E ~ Eκ = (3.5N/C)x̂. Compute the surface charge density on the left side of the slab. Select One of the Following: (a) −1.1 × 10−11 C/m2 (b) −3.1 × 10−11 C/m2 (c) −8.9 × 10−11 C/m2 (d) −5.8 × 10−11 C/m2 (e) −1.2 × 10−11 C/m2 1 Monday Homework Problem 5.3 The figure to the right shows a positive point charge with charge +Q in a cavity in a charged dielectric. Only the surfaces of the dielectric are charged. The surface of the cavity has a total charge +2Q. The outer surface of the dielectric has total charge −Q. What is the total charge enclosed in the Gaussian surface drawn (dashed line)? dielectric +Q Select One of the Following: (a) 0 (b) −Q (c) +2Q (d) +3Q (e) This cannot be determined because the cavity is not spherical. -σ +σ Conductor Monday Homework Problem 5.4 The figure to the right shows two parallel planes with equal and opposite surface charge densities, ±σ, σ = 0.1 µC m2 . Calculate the induced charge density on the left and right surface of the conductor. Select One of the Following: (a) σl = −0.1µC/m2 and σr = +0.1µC/m2 (b) σl = +0.1µC/m2 and σr = −0.1µC/m2 (c) σl = −0.05µC/m2 and σr = +0.05µC/m2 (d) σl = +0.05µC/m2 and σr = −0.05µC/m2 (e) σl = 0 and σr = 0 2 Monday Homework Problem 5.5 A uniform electric field is drawn to the right. A positively charged particle is placed in the field. In what direction does the potential energy of the particle increase? Select One of the Following: (a) to the left of the page +Q (b) to the right of the page (c) to the bottom of the page (d) to the top of the page (e) The direction of increase of electric potential energy cannot be determined from the information given. ~ = Cr2 r̂ Monday Homework Problem 5.6 A non-uniform radial charge distribution produces an electric field of E N 2 ~ for r > 5.0cm and E = 0 for r < 5.0cm, where C = 1700 C /m is a constant. What is the potential difference between a point r = 10.0cm and the center of the distribution, ∆Vr,0 ? Select One of the Following: (a) +0.50V (b) +3.50V (c) +1.25V (d) +2.25V (e) +2.3V Monday Homework Problem 5.7 A region of space contains an electric field ~ = − 2γ ẑ E z2 2 where γ = 120 Nm C . Compute the potential difference, ∆Vab (including the appropriate sign) between the point a = 3m and the point b = 5m along the z-axis. Select One of the Following: (a) +60V (b) −60V (c) −32V (d) +32V 3 Monday Homework Problem 5.8 The electric potential in a region of space has the value V (x) = −Γx cos(ax) where Γ is a constant. Compute the electric field in this region. Select One of the Following: ~ = (Γ cos(ax) + aΓ sin(ax))x̂ (a) E ~ = (Γ cos(ax) − aΓ sin(ax))x̂ (b) E ~ = Γ cos(ax)x̂ (c) E ~ = (d) E −Γx2 2 sin(ax)x̂ ~ = (Γ cos(ax) − (e) E Γx2 2 Γ sin(ax))x̂ ~ = (Γ cos(ax) − axΓ sin(ax))x̂ (f) E Monday Homework Problem 5.9 Four +4.0µC point charges are placed on the corners of a square with 8.0m sides. Find the potential difference between the center of the square and a point at infinity, ∆V∞0 . Select One of the Following: (a) 0 (b) 3.1 × 102 V (c) 4.2 × 104 V (d) 2.5 × 104 V (e) 6.7 × 106 V 4 Monday Homework Problem 5.10 The figure to the right shows three points in an electric field. The potentials of the points obey the relationship VA > VB > VC . The potential decreases uniformly from points A to C. A positively charged particle is constrained to move along the line drawn. If the particle is released from rest at point B, which of the following best describes its motion? A Select One of the Following: (a) The particle stays at rest at point B. (b) The particle moves toward point A with constant speed. (c) The particle moves toward point A with decreasing speed. (d) The particle moves toward point A with increasing speed. (e) The particle moves toward point C at a constant speed. (f) The particle moves toward point C with decreasing speed. (g) The particle moves toward point C with increasing speed. 5 B C Name: Lab Day/Time: Wednesday Homework 5 Electric Potential Homework is due at the beginning of the Wednesday lecture. It must be handwritten, not typeset. The multiplechoice answers must be circled. In the space after the problem, a short justification of each multiple-choice the answer must be included. The open-response answers must be worked out clearly using good physics presentation and will be graded on correctness and how carefully the work is explained. The problems should be worked in the space after the problem on the assignment printout; additional paper may be used if needed. No credit will be given for answers without appropriate supporting work. Minimum good presentation requires the following: (1) Symbolic expression for any formula, (2) Manipulation of symbolic expressions, not numeric expressions, (3) Substitution of numbers with units, (4) Reporting final answers with correct units and vector expressions, (5) Enough English description to allow the reader to have some idea what you are doing without looking at the math. Multiple Choice Problems The questions in this section are to be answered by circling the correct multiple-choice answer AND providing a short justification of your answer in the space after the problem.. Wednesday Homework Problem 5.1 Select the choice below that best explains how the induced charge on a conductor and the bound charge on a dielectric differ atomically. Select One of the Following: (a) Both are identical atomically. (b) Induced charge on a conductor involves motion of charge over macroscopic distances whereas bound charge on a dielectric only requires charge motion over atomic distances. (c) In a dielectric, the field causes the atoms to completely come apart. In a conductor, the atoms only lose an electron. (d) Induced charge is caused by electrons; bound charge by protons. (e) In a conductor, all charge goes to the surface. In a dielectric, only part of the charge goes to the surface. (f) Bound charge on a dielectric involves motion of charge over macroscopic distances whereas induced charge on a conductor only requires charge motion over atomic distances. (g) Induced charge involves only atoms; bound charge molecules. 1 Wednesday Homework Problem 5.2 A negative point charge with charge −Q is placed and held in the center of a grounded conducting box as shown to the right. What is the total charge on the outer surface of the conducting box? conductor -Q Select One of the Following: (a) 0 (b) +Q (c) −Q (d) +Q/2 (e) −Q/2 Wednesday Homework Problem 5.3 Two thin spherical uniform shells of charge each have charge Q and radius a and b, respectively, as shown to the right. Calculate the potential difference ∆V∞,b between a point at infinity and the outer shell. +Q b Select One of the Following: +Q a Q (a) 4πǫ0  1 1 − a b   1 1 − b a   1 2Q (c) 4πǫ0 a + b   2Q 1 (d) 4πǫ0 b   2Q 1 (e) − 4πǫ0 b Q (b) 4πǫ0  I II III path of integration 2 Wednesday Homework Problem 5.4 Two 3.0nC point charges are at ±15.0cmx̂. What is the potential difference, ∆V∞0 , between a point at infinity and the origin? Select One of the Following: (a) 0 (b) +2400V (c) −2400V (d) +360V (e) −360V (f) +7.2V (g) −7.2V Wednesday Homework Problem 5.5 A region of space contains an electric field ~ = −γy 3 ŷ E N where γ = +200 Cm 3 . Compute the potential difference, ∆Vab (including the appropriate sign) between the point a = 2m and the point b = 3m along the y-axis. Select One of the Following: (a) −3250V (b) +3250V (c) −950V (d) +950V 3 Open Response Questions Wednesday Homework Problem 5.6 The figure to the right shows a neutral spherical conductor and two +Q points charges. conductor (a)Draw the field map using 4 lines per charge. Draw the location of any induced charge. DRAW THE FIELD MAP ON ANOTHER SHEET OF PAPER. (b)Draw at least 8 equipotentials. Draw the equipotentials as dashed lines. (c)Select two of your equipotentials and clearly label the one at higher potential, HIGHER, and the one at lower potential LOWER. Explain how you determined which potential was higher and lower. +Q 4 +Q Wednesday Homework Problem 5.7 Three infinite parallel planes of charge have surface charge densities 3σ, −σ, and −2σ, as drawn. The electric field if the conductor and dielectric were ~ 0 = 3σ x̂ and E ~ 0 = 2σ x̂ (the ”0” is a superscript not present is E I II ǫ0 ǫ0 meaning ”naught”, not an exponent) . x −σ +3σ (a)Calculate the fields with the conductor and dielectric present. conductor −2σ dielectric (b)Draw the electric field and induced and bound charge densities; let ǫσ0 be 4 lines and use κ = 2 for the drawing. (c)Compute the induced surface charge densities on the left and right surfaces of the conductor. (d)Compute the bound charge densities on the left and right surfaces of the dielectric. (e)Calculate the potential difference ∆Vac assuming the conductor and dielectric completely fill the regions I and II respectively. 5 a b d1 d2 I II c Wednesday Homework Problem 5.8 Consider a spherical volume of charge of outer radius b, inner radius a, and uniform volume charge density ρ > 0. Compute the electric potential difference between a point at infinity and the center of the charged sphere. Air + Air + Ia Air I + II + b III Path of Integration 6 Wednesday Homework Problem 5.9 A total charge of +Q is placed on a solid conducting sphere of radius c. A neutral spherical conducting shell, centered on the origin, of inner radius a and outer radius b, is placed so that it surrounds the sphere and is concentric with it. Air Conductor Air + (a)Draw the electric field lines for all regions. (b)What is the surface charge density on the inner surface of the shell? (c)Use Gauss’ Law to find the electric field for all points in space as a function of r, which is the distance from the center of the sphere. 7 + Conductor + + a + b c + +
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Running head: Homework on electrical potential

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1

Homework on electrical potential
2
Question 5.1
If a positive or a negative charge are introduced inside a conductor, a surface charge is set up in a
conductor which then creates an electric field which exerts force on the conductor charges and pushes
them away from one another to the conductor surface and when they reach a conductor surface, they
spread away such that charges and electric field inside a conductor vanish (Fernandez, 1977).

Answer = (d) A surface charge is set up that creates an electric field which cancels the applied
field.
Question 5.2

surface charge density on the left side of the slab = ∇ ⋅ P.
P = χ ε0 E
Where χ = scalar quantity = 1
ε0 =Electric constant =8.854187817*10^-12C2/NM2
E = electric field
P = polarization density
Hence polarization density outside the slab = χ ε0 E where E= outside electric field
1*8.854187817*10^-12 *10 = 8.854187817*10^11C/m2
And polarization density inside the slab = χ ε0 E where E= inside electric field
1*8.854187817*10^-12* 3.5 = 3.0989*10^-11 C/m2
Surface charge density on the left side = Inside polarization charge density – outside charge
density
3.0989*10^-11 -8.854187817*10^-11 = -5.7551 = -5.8 C/m2
Answer = (d) −5.8 × 10^−11C/m2

Homework on electrical potential
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Question 5.3
Total charge = total surface charge of a cavity + total charge of a point in a cavity +total charge
of outer surface of dielectric
Total charge of a point in a cavity =+Q.
Total charge of a surface of the cavity = +2Q.
Total charge of outer surface of a dielectric = −Q.
Total charge = =(+Q) +(+2Q) +(-Q) = +2Q
Answer = (c) +2Q.
Question 5.4
Induce charge = σ (1+ (±1/𝐾)
Wh...


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