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Name: Lab Day/Time:

Homework 2 Electric Field

Homework is due at the beginning of the Wednesday lecture. It must be handwritten, not typeset. The multiple- choice 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.

Early Questions

The questions in this section are over material that will be covered by Friday. These may be worked before the other questions.

Homework Problem 2.1 A negatively charged rod is brought near the bolt of an electroscope and the following is observed: What is the sign of the net charge of the electroscope?

Select One of the Following:

(a) The electroscope is positively charged.

(b) The electroscope is negatively charged.

Homework Problem 2.2 When you charge an electroscope by connecting it to a charged conductor, what is actually physically transferred?

Select One of the Following:

(a) electrons

(b) protons

(d) atoms

(e) protons and electrons

(f) electrons and neutrons

(g) nothing

Homework Problem 2.3 An electrophorus is constructed of a metal plate with an insulating handle and an unconnected dielectric plate. It is initially neutral when it is first pulled out of the lab cabinet. How is a net charge introduced into the apparatus?

Select One of the Following:

(a) The dielectric plate draws charge from the air.

(b) The dielectric plate must be rubbed with an insulating material.

(d) The dielectric plate automatically has a substantial net charge because of the way it is constructed.

(e) Charge must be sprayed on the dielectric plate with a charge gun.

Homework Problem 2.4 Two point charges each experience an acceleration with a magnitude of a due to the electric force between them when they are separated by a distance equal to r. What accelerations do they experience when they are separated by a distance of r/2?

Select One of the Following:

(a) a/4 (b) a/2 (c) 2a (d) 4a (e) a

Homework Problem 2.5 Two neutral spheres are suspended from light strings and brought near each other. No deflection is observed. Why doesn’t the gravitational attraction of the objects cause a noticeable deflection?

Select One of the Following:

(a) The objects contain like amounts of positive and negative masses.

(b) There is no gravitational attraction. Gravitational forces only exist between things like planets and stars.

(d) The gravitational force between the spheres is too weak to be observed compared to the gravitational force between each sphere and the earth.

(e) An object must be charged for there to be a gravitational force.

Homework Problem 2.6 The two protons in the helium nucleus are about 1 × 10−15m apart. What is the magnitude of the electric force one proton exerts on the other?

Select One of the Following:

(a) 200N

(b) 1 × 10−20N

(d) 4 × 10−6N

(e) 3 × 109N

Homework Problem 2.7 If DNA has a charge of 0.3e per base pair in solution and there are 3×109 base pairs in a human genome, then the total charge of the human genome in solution is 1.4 × 10−10C. If the DNA molecule is placed in an electric field of 100, 000N

C , what would the acceleration of the DNA molecule be? The mass of a

DNA molecule is on the order of 3 × 10−15kg.

Select One of the Following:

(a) 2 m s2

(b) 3 × 103 m s2

(d) 5 × 109 m s2

(e) 4 × 10−20 m s2

Homework Problem 2.8 The electric field due to a point charge has a magnitude of E at a distance r from the point charge. What is magnitude of the electric field at a distance 2r away from the point charge?

Select One of the Following:

(a) E (b) 2E (c) 4E (d) E/2 (e) E/4

Homework Problem 2.9 The figure to the right shows two charged particles with equal but opposite charges ±Q. The two particles are a distance d apart and the negatively charged parti- cle is a distance d from the point a. What is the direction of the electric field at the point a?

a x

-Q +Q

Select One of the Following:

(a) The electric field is zero.

(b) The electric field points in the positive x direction.

(d) The electric field points in the positive y direction.

(e) The electric field points in the negative y direction.

Multiple-Choice Questions

The questions in this section are over material that will be covered by the Monday before the assignment is due.

Homework Problem 2.10 A −3.0nC point charge is located at the point ~r1 = (−5.0cm, 3.0cm, 5.0cm). Compute the electric field at the point 3.0cmx̂ − 4.0cmŷ.

Select One of the Following:

(a) ~E10 = 0.20 N

C (−0.80, 0.10, 0.59)

(b) ~E10 = 2.0 × 10 3 N

C (−0.68, 0.60, 0.43)

C (−0.68, 0.73, 0)

(d) ~E10 = 1.3 × 10 2 N

C (1.0, 0, 0)

(e) ~E10 = 2.0 × 10 7 N

C (−0.68, 0.60, 0.43)

Homework Problem 2.11 Suppose you want to float a truck with a mass of 10, 000kg in earth’s gravity by placing a charge of 3C on the truck and floating it above an infinite plane with surface charge density σ. What must σ be?

Select One of the Following:

(a) 5.8 × 10−7C/m2

(b) 1.7 × 10−5C/m2

(d) 3.0 × 10−3C/m2

(e) 2.1 × 10−2C/m2

Homework Problem 2.12 Lightning strikes the power lines, briefly transferring a linear charge density of 1.0 × 10−3 C

m . Model the power lines as a single infinite straight uniform line charge. Calculate the magnitude of the

electric field at the ground a distance of 5.0m from the wire.

Select One of the Following:

(a) 3.6 × 105 N C

(b) 1.8 × 106 N C

(d) 7.2 × 105 N C

(e) 3.5 × 108 N C

Homework Problem 2.13 The electric field in a region of space is given by ~E(~r) = (100N C , 50N

C , −x2(N

C /m2)).

Note, this electric field can not be generated by a static charge, we’re just playing with vector functions. Assume two significant figures. Compute the strength(magnitude) of this electric field at a point 5m along the positive x-axis.

Select One of the Following:

(a) 141N C

(b) 250N C

(d) 2500N C

(e) 110N C

Homework Problem 2.14 The figure to the right shows two infinite planes of charge. The left plane has charge density σl = +3σ. The right plane has uniform surface charge density σr = −σ. Compute the electric field at P if σ = 0.0300µC/m2

Select One of the Following:

(a) ~EP = 6.78 × 10 3 N

C x̂

(b) ~EP = −6.78 × 10 3 N

C x̂

(d) ~EP = 3.89 × 10 3 N

C x̂

x+3σ − σ

Homework Problem 2.15 A positively charged particle with charge +q and a negatively charged particle with charge −2q are placed along the y axis as drawn to the right. The two particles are equidistant from the origin. The drawing is divided into three regions by the dashed lines. Select the region or regions where there is a point with zero electric field (except at infinity).

-2q

Region 1

Region 2

Region 3

Select One of the Following:

(a) Region 1 only.

(b) Region 2 only.

(d) Regions 1 and 3.

(e) The electric field is non-zero at all points (except at infinity) in all regions.

Open Response Questions

All questions in this section must be worked. One of the questions will be graded.

Homework Problem 2.16 Explain how you would build and use an electrophorus to charge a leaf electroscope by charge transfer. Be careful to draw each stage of the charging process, including the charge on each object.

Homework Problem 2.17 In the space below, draw a coordinate system in centimeters, draw a dot and label it 1 at location (3cm, 1cm) and another dot labelled 2 at (4cm, 5cm). Those of you complaining that you don’t have rulers shouldn’t really do these at the last minute. On the print options dialog, select the page scaling option “None” instead of “Shrink to fit” to get an actual centimeter grid.

(a)On the diagram, draw and label the position vector ~r1 and ~r2 . Explain how you did this.

(b)Draw and label the displacement vector ~r12.

(c)Using a ruler, measure the distance from the origin to point 1, d1. Measure the distance from the origin to point 2, d2, and the distance from point 1 to point 2, d12.

(d)Compute |~r1|, |~r2|, and |~r12|. Compare these values with the distances measured in the previous step.

Homework Problem 2.18 Two −1nC charges, q1 and q2, are at ~r1 = −10cmx̂ and ~r2 = +10cmx̂. A third charge q3 = 2nC is located at ~r3 = 10cmŷ. Compute the electric field at the point ~r0 = 5cmŷ.

Homework Problem 2.19 A golf tube through the point 5.0cmŷ (modeled as an infinite line of charge) and parallel to the z-axis carries a linear charge density of −0.50µC

m .

A charged pith ball with a charge of −50.0nC is located at the origin. Consider the electric field at the point P located at 5.0cmx̂.

(a)Compute the electric field of the golf tube at point P .

(b)Compute the electric field of the pith ball at point P .

(c)Compute the total electric field at point P.

(d)Draw the electric field vectors of each object and the total electric field at point P .

golf tube

pith

ball