PHYS112 WVU Gauss Law Conductors and Dielectrics

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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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Monday Homework 4 Gauss’ Law with Conductors and Dielectrics

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 4.1 A cube has a uniform electric field normal to all six faces. The strength of

the field is 6

N

C

outward on face 1, 6

N

C

outward on face 2, 3

N

C

inward on face 3, 6

N

C

outward on face 4, 6

N

C

inward

on face 5, and 10 N

C

inward on face 6. Does the cube contain a net charge? If it does, what is the sign of the net

charge in the cube?

Select One of the Following:

(a) positive

(b) negative

(c) The net charge in the cube is zero.

Monday Homework Problem 4.2 A Gaussian surface encloses zero net charge. Must the electric field be zero

at all points on the surface?

Select One of the Following:

(a) no

(b) yes

Monday Homework Problem 4.3 An infinite plane of charge with uniform charge density ?1 = ? occupies the

y ? z plane through the origin. A parallel plane through x = 1cm has charge density ?2 = ??/2. Compute the

Name: Lab Day/Time: Monday Homework 4 Gauss’ Law with Conductors and Dielectrics 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 4.1 A cube has a uniform electric field normal to all six faces. The strength of N N N N the field is 6 N C outward on face 1, 6 C outward on face 2, 3 C inward on face 3, 6 C outward on face 4, 6 C inward N on face 5, and 10 C inward on face 6. Does the cube contain a net charge? If it does, what is the sign of the net charge in the cube? Select One of the Following: (a) positive (b) negative (c) The net charge in the cube is zero. Monday Homework Problem 4.2 A Gaussian surface encloses zero net charge. Must the electric field be zero at all points on the surface? Select One of the Following: (a) no (b) yes Monday Homework Problem 4.3 An infinite plane of charge with uniform charge density σ1 = σ occupies the y − z plane through the origin. A parallel plane through x = 1cm has charge density σ2 = −σ/2. Compute the electric field in the region between the planes. Select One of the Following: (a) 3σ/2ǫ0 x̂ (b) σ/4ǫ0 x̂ (c) 3σ/4ǫ0 x̂ (d) −σ/4ǫ0 x̂ (e) -3σ/4ǫ0 x̂ 1 Monday Homework Problem 4.4 A spherical balloon has a radius of 40cm and produces an electric field of magnitude 2 N C radially outward at the balloon’s surface. If we assume the charge is mostly at the surface of the balloon, forming a uniform thin shell of charge, calculate the surface charge density of the balloon. Select One of the Following: (a) 1.8 × 10−11 C/m2 (b) −2.1 × 10−16 C/m2 (c) 4.5 × 10−11 C/m2 (d) −1.1 × 10−1 C/m2 (e) −1.8 × 10−9 C/m2 Monday Homework Problem 4.5 The figure to the right shows two charged spherical shells. The inner shell has radius a and charge density σa = −2σ. The outer shell has radius b and charge density σb = +3σ. Calculate the electric field in Region II between the two shells (a < r < b). y III II Select One of the Following: a I Air (a) 0 (b) (c) (d) (e) (f) 2a2 σ − r̂ ε0 r 2 a2 σ + r̂ 2πε0 r2 5πa2 σ − r̂ 4πε0 r2 πa2 σ + r̂ 4πε0 r2 −2πa2 σ + 3πb2 σ r̂ 4πε0 r2 Air Air 2 x b Monday Homework Problem 4.6 Two infinite parallel planes of charge with uniform surface charge densities are parallel to the x − z plane and equally spaced about the origin. The planes pass through the points ±1cm. The plane passing through +1cmŷ has surface charge density 32 σ. The plane passing through −1cmŷ has surface charge density 5σ. The planes are drawn to the right. Compute the electric field at the origin. y + 32 σ Select One of the Following: x (a) +13σ/4ǫ0 ŷ +5 σ (b) −13σ/4ǫ0 ŷ (c) +13σ/2ǫ0 ŷ (d) −13σ/2ǫ0 ŷ (e) +7σ/4ǫ0 ŷ (f) −7σ/4ǫ0 ŷ (g) +7σ/2ǫ0 ŷ (h) −7σ/2ǫ0 ŷ Monday Homework Problem 4.7 A positively charged particle is placed in a uniform electric field directed toward the negative y direction as drawn to the right. Rank the relative magnitudes of the electric force on the positive charge if it is placed at points a, b, c, and d. y c Select One of the Following: (a) b < a = d < c a (b) c = d > a = b (c) c > a = d > b b (d) c < a = d < b (e) a = b = c = d (f) c < a < d < b 3 d x Monday Homework Problem 4.8 The figure to the right shows two charged particles: the particles have equal but opposite charge ±q. They are equidistant from the origin and are placed along the y-axis. What is sign of the x component of the electric field at a point P on the x-axis? y +q Select One of the Following: (a) The x component is zero. (b) The x component is positive. P (c) The x component is negative. x -q Monday Homework Problem 4.9 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 × 10−7 C/m2 (b) 1.7 × 10−5 C/m2 (c) 3.4 × 10−5 C/m2 (d) 3.0 × 10−3 C/m2 (e) 2.1 × 10−2 C/m2 Monday Homework Problem 4.10 A particularly large solar flare erupts on the sun’s surface sending a burst of C solar wind directly at earth. As the wind reaches earth, it briefly transfers a linear charge density of 2.0 × 10−5 m along the power lines. Modelling the power lines as single infinite straight uniform line charges, calculate the magnitude of the electric field at the ground a distance of 5.0m from the wire. Select One of the Following: (a) 1.4 × 104 N C (b) 3.6 × 105 N C (c) 3.6 × 104 N C (d) 7.2 × 104 N C (e) 1.1 × 106 N C 4

Tutor Answer

madushan
School: Boston College

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