Download Set #3 - McMaster Physics and Astronomy

Practice Problems 3
1. 1. A uniform electric field 26.0i + 32.7j intersects a surface of area 0.58 m2. What
is the flux through this area if the surface lies in the yz-plane?
Answer: 1.51e+01 N*m^2/C
2. What is the flux through this area if the surface lies in the xz-plane?
Answer: 1.90e+01 N*m^2/C
3. What is the flux through this area if the surface lies in the xy-plane?
Answer: 0 N*m^2/C
4. A flat surface having an area of 3.08 m2 is rotated in a uniform electric field of
magnitude E = 6.20×105 N/C. Determine the electric flux through this area when
the electric field is perpendicular to the surface.
Answer: 1.91e+06 N*m^2/C
5. Determine the electric flux through this area when the electric field is parallel
to the surface.
Answer: 0.00e+00 N*m^2/C
6. Four closed surfaces, S1 through S4, together with the charges -xQ (x = 4), Q,
and -Q are sketched in the figure below.
Calculate the electric flux through each surface (in units of Q/ε0, from 1 through
4).
Answer: -3.00E+00 0.0 -4.00E+00 0.0
7. An infinitely long line charge having a uniform charge per unit length
λ=1.61×10-6 C/m lies a distance d=0.245 m from point O, as shown.
Determine the total electric flux through the surface of a sphere of radius
R=0.542 m centred at O resulting from this line charge.
Answer: 1.76e+05 N*m^2/C
8. A point charge Q = 4.69 µC is located at the center of a cube of side L =
0.126 m. In addition, six other identical point charges having q = -1.01 µC are
positioned symmetrically around Q, as shown in the figure below.
Determine the electric flux through one face of the cube.
Answer: -2.58E+01 kN*m^2/C
9. An insulating sphere is 7.24 cm in diameter and carries a 5.08 µC charge
uniformly distributed throughout its interior volume. Calculate the charge
enclosed by a concentric spherical surface with radius r = 1.93 cm.
Answer: 7.70E-07 C
10. Calculate the charge enclosed by a concentric spherical surface with radius r =
6.20 cm.
Answer: 5.08E-06 C
11. A closed surface with dimensions a = b = 0.435 m and c = 0.590 m is located
as shown in the figure below.
The electric field throughout the region is nonuniform and given by E = (2.83 +
2.02x2)i N/C, where x is in meters. Calculate the net electric flux leaving the
closed surface.
Answer: 3.29E-01 N*m^2/C
12. What net charge is enclosed by the surface?
Answer: 2.92E-12 C
13. For the configuration shown in the figure below, suppose that a = 4.85 cm, b
= 19.9 cm, and c = 24.0 cm.
Furthermore suppose that the electric field at a point 7.8 cm from the center is
3.73×103 N/C radially inward, while the electric field at a point 52.2 cm from the
center is 2.07×102 N/C radially outward. From this information, calculate the
charge on the insulating sphere.
Answer: -2.52E+00 nC
14. Calculate the net charge on the hollow conducting sphere.
Answer: 8.80E+00 nC
15. A square plate of copper with 46.9 cm sides has no net charge and is placed in
a region of uniform electric field of 79.9 kN/C directed perpendicularly to the
plate. Calculate the charge density of each face of the plate.
Answer: 7.07E-07 C/m^2
16. Calculate the total charge on each face.
Answer: 1.56E-07 C
17. [1 point, 10 tries]
A cylindrical shell of radius 5.35×10-2 m and length 2.30 m has its charge
uniformly distributed on its curved surface. The magnitude of the electric field at
a point 0.199 m radially outward from its axis (measured from the midpoint of the
shell) is 3.56×104 N/C. Use approximate relations to find the net charge on the
shell. [SER-24.28a]
Answer: 9.06e-07 C