Quizbank/Electricity and Magnetism (calculus based)/QBCh6

QB153086031104

QB:Ch 6:V1
QB153086031104 1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.2 m. The other four surfaces are rectangles in y=y0=1.7 m, y=y1=4.6 m, z=z0=1.4 m, and z=z1=4.5 m. The surfaces in the yz plane each have area 9.0m2. Those in the xy plane have area 6.4m2 ,and those in the zx plane have area 6.8m2. An electric field of magnitude 15 N/C has components in the y and z directions and is directed at 31&deg; from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
 * a) 3.959E+01 N&middot;m2/C
 * b) 4.354E+01 N&middot;m2/C
 * c) 4.790E+01 N&middot;m2/C
 * d) 5.269E+01 N&middot;m2/C
 * e) 5.796E+01 N&middot;m2/C

2) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=5, y=0), (x=0, y=7), and (x=5, y=7), where x and y are measured in meters. The electric field is, $$\vec E=3y^{2.9}\hat i +3x^{1.6}\hat j +4y^{2.5}\hat k$$
 * a) 4.286E+03 V&middot;m
 * b) 4.714E+03 V&middot;m
 * c) 5.186E+03 V&middot;m
 * d) 5.704E+03 V&middot;m
 * e) 6.275E+03 V&middot;m

3) A non-conducting sphere of radius R=3.5 m has a non-uniform charge density that varies with the distnce from its center as given by &rho;(r)=ar1.5 (r&le;R) where a=2 nC&middot;m-1.5. What is the magnitude of the electric field at a distance of 2.2 m from the center?
 * a) 3.604E+02 N/C
 * b) 3.964E+02 N/C
 * c) 4.360E+02 N/C
 * d) 4.796E+02 N/C
 * e) 5.276E+02 N/C