Download PHYS 196 Class Problem 1

PHYS 196 Home Work 3B (Gauss Law)
1. A uniform electric field of magnitude 720N/C passes through a circular disk of radius 13cm . Find the
electric flux if its face is (a) perpendicular to the field line, (b) at 30 to the field line, and (c) parallel to
the field line.

2. A uniform electric field E is parallel to the axis of a hollow hemisphere of radius r . (a) What is the

electric flux through the hemispherical surface? (b) What is the result if E is perpendicular to the axis?
3. A point charge q is at the center of a cube of side a . What is the electric flux through one of the faces?
4. A spherical shell of radius 25cm has a surface charge density 48nC / m 2 . Find the electric field at a point
(a) just outside the surface, (b) in the interior, and (c) at a distance 50cm from the center.
5. A solid sphere of radius 25cm carries a total charge 72nC uniformly distributed over its volume. Find
the electric field (a) at a point just outside the sphere, and (b) at an interior point 10cm from the center.
6. Two concentric thin spherical shells of radius R1 and R2 with R1  R2 carry uniformly distributed charge
Q1 and Q2 respectively. Use Gauss law to find the electric field at a point a distance r from the center, in
the three cases r  R2 , R2  r  R1 and R1  r .
7. A solid sphere of radius a carries a uniform charge distribution over its volume. The total charge is Q .
Use Gauss law to find the electric field at a point a distance r from the center in the two cases r  a and
ra.
8. Two coaxial infinitely long thin cylindrical shells of radius R1 and R2 with R1  R2 carry uniformly
distributed charge per unit length of 1 and 2 respectively. Use Gauss law to find the electric field at a
point a distance r from the axis, in the three cases r  R2 , R2  r  R1 and R1  r .
9. From a solid sphere of radius a with a uniform charge density  , a spherical volume of radius a 2 is
removed as shown. Find the magnitude and direction of the electric field at the center of the original
sphere.
10. The electron cloud in a hydrogen atom corresponds to a spherically symmetric charge distribution with
volume charge density    0e  2 r a where r is the distance from the center. Find the electric field as a
function of r .
1
Answers:
Q
1 Qr
,
2
40 r
40 a 3
1 1  2
1 1
,
, 0
8.
20 r
20 r
a
9.
6 0
1. 38.2 Nm2 / C, 19.1Nm2 / C, 0
7.
2. r 2 E , 0
3.
q
6 0
1
 0 a 3   2r 2 2r   2 r a 

 1e
10.
1  

4 0 r 2   a 2
a


4. 5400 N / C , 0, 1350 N / C
5. 1.04  104 N / C, 4140 N / C
1 Q1  Q2
1 Q1
,
, 0
6.
2
40 r
40 r 2
2