PROBLEMS - University Physics 2 - Homework 2 - Gauss's Law

 

PROBLEMS University Physics 2 Homework 2 – Gauss’s Law 1)

A rubber rubber ballo balloon on has has a single single point point charge charge in its inter interior ior.. Does the elec electric tric flux flux thro through ugh the balloon depend on the size and shape of the balloon? Explain.

2)

A positiv positive e charge charge Q and nega negative tive charge charge -Q are place placed d 1 m apart apart.. Gaussia Gaussian n surface surface A is wrapped around the positive charge. Gaussian surface B is wrapped around the negative charge. Gaussian surface C is wrapped around both charges. Gaussian surface D is inside Gaussian surface C but does not wrap around either of the two charges. Describe the flux through each surface as either positive, negative, or zero. Take the inward flux as negative.

3)

In p probl roblem em #2, #2, a third third charge charge Q is now now place placed d outsid outside e the the Gauss Gaussian ian surfa surface ce C. C. Describe Describe the flux through each surface as either positive, negative, or zero. Take the inward flux as negative.

4)

A spheric spherical al Gaussi Gaussian an surfac surface e enclos encloses es a point point charge charge Q with with Q at its its center center.. (a) If the point point charg charge e Q is moved moved from from the cent center er of the the sphere sphere to a point point away away from from (b)

the center, does the electric field at a point on the Gaussian surface change? Does Does the the total total flux flux through through the Gaussia Gaussian n surfac surface e change change? ? Explain Explain..

5)

A flat flat sh shee eett of of pap paper er of area area 0.25 0.25 m2 is oriented so that the normal to the paper is at an angle of 60° to a uniform electric field of magnitude 14 N/C. (a) What is the the magnitu magnitude de of the the elect electric ric flux flux tthrou hrough gh the the paper? paper? (b) What angl angles es betwee between n the normal normal to the the paper paper and the the electri electric c field field give a maximu maximum m and minimum electric flux through the paper?

6)

A flat sheet sheet is in the the shape shape of a rectangl rectangle e with with sides sides of lengt lengths hs 0.4 0.4 m and and 0.6 0.6 m. The sheet is immersed in a uniform electric field of magnitude 90 N/C that is directed at 20° from the plane of the sheet. What is the magnitude of the electric flux through the sheet?

7)

You meas measure ure an elec electri tric c fiel field d of of 1.25 1.25 X 10 106 N/C at a distance of 0.15 m from a point charge. (a) What What iis s the the magnit magnitud ude e of of the the char charge? ge? (b) What is is the electri electric c flux throu through gh the surfac surface e of a sphere sphere that that has this this charge charge at its its center and that has radius 0.15 m?

8)

Ac cube ube with with sides sides of lengt length h 10 cm is located located with with one one corner corner at the the origin origin and and it’s it’s volume volume located such that all coordinates of the interior of the cube have positive values for x, y, and z. A uniform electric field with magnitude 4 X 103 N/C is parallel to the xy-plane at an angle of 53.1° measured from the +x-axis toward the +y-axis. (a) What is the elect electric ric flux flux throu through gh each each of the the six sides sides of of the cube cube faces? faces? (b) What is the the total total electr electric ic flux flux throug through h all faces faces of the the cube? cube?

 

9)

Thre ree e poin intt char arg ges, Q1, Q2, and Q3, are enclosed by several surface areas as indicated below. What is the net electric flux through each surface? S1 Q1 S2 Q2 S3 Q1 and Q2 S4 Q1 and Q3 S5 Q1 and Q2 and Q3

10) A charged charged paint is spread in in a very thin uniform uniform layer over the surface of a plastic plastic sphere sphere of diameter 12 cm. The charge on the paint is -49 μC. What is the electric field (a (a)) just just in insi side de the the pai paint nt laye layer  r  (b (b)) ju just st out outsi side de the the pai paint nt laye layer  r  (c (c)) on the the sur surfa face ce of of the the pai paint nt lay layer  er  (d) 5 cm outs outsid ide e the the surfa surface ce of of the the paint paint layer  layer  11) A very long long uniform uniform line of charge has has charge charge per unit unit length 4.8 μC/m and lies along along the x-axis. A second long uniform line charge has charge per unit length 2.4 μC/m and is parallel to the x-axis at y=0.4 m. What is the net electric field (magnitude and direction) at the following points on the y-axis? (a) y=0.2 m (b) y=0.6 m 12) The electric electric field field 0.4 m from a very long uniform uniform line of charge charge is 840 N/C. N/C. What is the magnitude of the charge contained in a 2 cm section of the line? 13) A hollow hollow,, conducting conducting sphere with an outer outer radius of 0.25 m and an inner inner radius radius of 0.2 m -6 2 has a uniform surface charge density of 6.37 X 10  C/m . A charge of -0.5 μC is introduced at the center of the sphere. (a) What is the the new charge charge densi density ty on the the outsi outside de of the spher sphere? e? (b) What is the the elect electric ric flux just just outsid outside e the the sphere sphere? ? (c) What is is the electri electric c flux throu through gh a spherica sphericall surface surface just just inside inside the the inner inner surface surface of the sphere? 14) (a) (b)

(c)

At distanc distance of 0.2 field cm from from theN/C. center centWhat er of of aischarged cha conduct conducting sph with witthe h radius radius 0.1acm, the e electric is 480 therged electric fielding 0.6sphere cmere from center of the sphere? At a distanc distance e of 0.2 cm from from the axis axis of a very very long long charged charged condu conductin cting g cylinder cylinder with radius 0.1 cm, the electric field is 480 N/C. What is the electric field 0.6 cm from the axis of the cylinder? At a distan distance ce of 0.2 0.2 cm from from a large large uniform uniform shee sheett of charge charge,, the electr electric ic field field is 480 N/C. What is the electric field 1.2 cm from the sheet?

 

15) A solid conductin conducting g sphere with radius radius R that that carries positive charge Q is concentric concentric with with a very thin insulating shell of radius 2R that also carries charge Q. The charge Q is distributed uniformly over the insulating shell. (a) Find Find the electri electric c field field (magnitu (magnitude de and dire directio ction) n) in each each of the regio regions: ns: 0