Chipola Junior College

PHY 2049 : E-Force Field Practice

1. Consider an infinitely long cylindrical shell of uniform surface charge s and radius R. An infinite line of uniform charge described by a linear charge density l lies along the axis of the cylinder as shown below.

           

a) Find the electric field at all points within the cylindrical shell (that is, r<R).

b) Calculate the electric field outside of the cylindrical shell, for r>R.

 

2. Consider the distribution of point charges shown below. The coordinate axes are marked in centimeters.

                       

a) Find the electric field at the origin due to this distribution of charges.

 

b) Calculate the electric field on the y-axis at y=4 cm.

c) Find the force on an additional charge of 5x10-8 C if it is placed at the origin.

4. Consider the distribution of charges shown below. The distribution consists of an infinite solid cylinder of charge with radius R characterized by a volume charge density of r (C/m) and a finite line of charge (length L and charge +Q) oriented perpendicularly a distance a away.

 

 

 

 

 

 

                        +Q

 

 

 

Find the electric field at a point P on the axis of the finite line of charge in between the two charged lines. Define the distance from P to the infinite cylinder to be B.

 

4. Consider the distribution of point charges shown below. The coordinate axes are marked in centimeters.

                                                 (cm)

a) Find the electric field at the origin for this distribution of charges.

b) Calculate the electric field on the y-axis at y=7 cm.

c) Find the force on an additional charge of qo=5x10-8 C if it is placed at the origin.

 

3. A conducting solid sphere of radius a has a total charge of +Q on its outer surface. A hollow uncharged conducting sphere of inner radius b and outer radius c is placed around the original charge as shown below

                                                           

a) Calculate the electric field at all points in space.

b) Find the surface charge density on the inner and outer surface of the hollow conductor.

c) What is the electric flux through any surface enclosing the charge?

 

5. For the spherical charge distribution below, the inner conductor has a radius R with a charge of +Q distributed on its surface, and the outer shell of charge has an inner radius of R and outer radius of 3R. The shell is made of a material with a charge density r.

 

 

 

 

 

 

 


a)      Calculate the electric field within the inner conductor.

b)      Find the electric field within the shell of charge.

c)      What is the electric field outside of the shell, for r >3R?

d) Find the surface charge density s on the outside of the inner conductor?

 

6. Consider the continuous distribution of charges shown below: a hoop of charge with its axis along the x-axis lies in the y-z plane.  The hoop has a total charge of Q and a radius 3a.  The axis of an infinite hollow cylindrical shell with inner radius a and outer radius 2a lies a distance of 6a directly above the x-axis. The cylindrical shell is made out of a material with a charge density of r.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


Calculate the electric field at point P, which is located on the x-axis a distance of 10a from the origin.