Physics 2420 In-Class Problems:
Electrical Energy and Method of Images

1. Charges are arranged as shown below. What is the electrostatic potential energy of each configuration?

2. (a) The side of the square has length L.

   

   (b) The separation of the charges is L.

   

3. Two point charges of q₁ = 3.0 μC and q₂ = 4.0 μC are situated at the opposite corners of a rectangle as shown below. The short side has length L = 0.25 m. Find the total potential at points A and B. If a free particle of charge q_f = 1.0 μC and mass M = 15 g has speed v_A = 2.50 m/s at point A and it follows the indicated path, what will be its speed at point B?

   

4. Find the electrostatic potential difference between points A and B which are distances r_A = 2.0 m and r_B = 1.0 m from an infinitely long thin wire with λ = 1.0 μC/m. The result E = λ/2pe ₀r is useful. If an electron (q = –e = –1.602 × 10^–19 C and mass me = 9.11 × 10^–31 kg) is released from rest at point A, what is it's speed at point B?

5. Find the electrostatic potential between points A and B which are distances r_A = 2.0 m and r_B = 1.0 m from an infinitely large thin plate with Σ = 1.0 μC/m² . The result E = Σ/2e ₀ is useful. If an electron (q = –e = –1.602 × 10^–19 C and mass m_e = 9.11 × 10^–31 kg) is released from rest at point A, what is it's speed at point B?

6. The electric field due to a spherical charge distribution is given by

   

   Find the energy stored in the field.

7. The electric field due to a spherical charge distribution is given by

   

   Find the energy stored in the field.

8. A thick conducting spherical shell has out radius R and thickness a. A charge 4Q is placed on the conductor. Then a charge –2Q is placed at the centre of the shell. Find and sketch the electric field as a function of r.

9. A charge Q is placed near two very large conducting plates which meet at a right angle as shown in the diagram below. Use the method of image to determine the components of the force exerted on the charge by the wall. Determine the induced charge density s on each wall.

   

10. A charge Q is placed a distance a from the centre of a conducting thin spherical shell of radius R (a < R). The shell is kept at zero potential. Find the location, sign, and magnitude of the image charge in this situation. What is the force exerted on the original charge by the shell? Determine the induced charge density s (q) on the shell.

    

Questions? mike.coombes@kwantlen.ca