CairoUniversity 2nd Year Electronics & Comm.

Faculty of Engineering Electromagnetic Fields & Waves

Exercise Sheet #1

  1. Two point charges Q1 and Q2 are located at (1,2,0) and (2,0,0) respectively. Find the relation between Q1 and Q2 such that the total force on a test charge at the point (-1,1,0) will have a) no x-component, b) no y-component.
  2. Two very small conducting spheres, each of mass 0.1 g, are suspended at a common point by very thin non-conducting threads of a length 0.2 m. A charge Q is placed on each sphere. The electric force of repulsion separates the spheres, and equilibrium is reached when the suspending threads make an angle of 10. Assuming a gravitational force of 9.8 N/kg and a negligible mass for the threads, find Q.
  3. Find the force between a charged circular loop of radius b and uniform charge density and a point charge Q located on the loop axis at a distance h from the plane of the loop. What is the force when h>b and when h=0? Plot the force as a function of h.
  4. A flat circular disk of radius R carries a uniform surface charge density. A concentric circular hole of radius b is drilled in the disk. If the disk lies in the x-y plane and its center is at the origin, show that the electrostatic field at any point on the axis of the disk (z-axis) is given by:
  1. A line charge of uniform density in free space forms a semi-circle of radius b. Determine the magnitude and direction of the electric field intensity at the center of the semi-circle.
  2. An infinitely long cylindrical shell of radii 3 cm and 5 cm is carrying a charge of uniform density 10-6 C/m3. Calculate E at all radii, and plot vs. at the central region.
  3. A spherical cavity of radius ½ R is constructed inside a charged sphere of radius R and uniform charge density C/m3. The center of the cavity is at a distance ½ R from the center of the sphere. Obtain an expression for the electric field inside the cavity.
  4. Calculate E and D at all points of space due to a system formed of free charges +Q and -Q uniformly distributed over two concentric spherical surfaces of radii R1 and R2 respectively in the following two cases:

i)No dielectrics are present.

ii)In the presence of a homogeneous and isotropic layer of dielectric of radii a and b and of dielectric constant where R1 < a < b < R2.

Plot the lines representing E and those representing D.

  1. Two infinitely long cylindrical layers of dielectrics of inner radii 10 cm and 15 cm and thickness 5 cm, are placed coaxially with a free cylindrical charge, the same as that in problem (6). Calculate:

i)The polarization charge density on the interface of the two dielectrics.

ii)The polarization vector at radii 12 cm and 16 cm.

The inner dielectric has and the outer dielectric has .