Physics 2420 In-Class Problems: Electric Potential from Electric Fields

1. The electric field due to a charged spherical shell is given by

   

   Determine V as a function of a where a is the distance from the centre of the sphere. Plot V as a function of a.

2. The electric field due to a large thin plate is given by

   

   Determine V as a function of a where a is the distance from the centre of the plate. Plot V as a function of a.

3. The electric field for a flat plate of charge density s is

   

   Determine V as a function of a where a is the distance from the centre of the plate. Plot V as a function of a.

4. The electric field due to a large plate was given in the previous question. A capacitor consists of two identical plates with equal but opposite charge distributions.
   (a)Find the net field just to the right of the centre of the capacitor. Do the same on the left side. Find the net electric field at a point between the place a distance a from the positive plate. Show that is R >> d that the E_net = 0 outside the plates and E_net = Σ/e ₀ between the plates.
   (b) Find the potential difference between the plates. Show that the potential difference between the plates is directly proportional to the separation d of the plates when R >> d.

5. The electric field due to a very long cylinder is given by

   

   Determine V as a function of a where a is the distance from the centre of the cylinder. Plot V as a function of a.

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

   

   Determine V as a function of a where a is the distance from the centre of the spherical charge distribution. Plot V as a function of a.

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

   

   Determine V as a function of a where a is the distance from the centre of the spherical charge distribution. Plot V as a function of a.

8. The electric potential over a certain region is given by V = 3x²y–4xz–5y² volts. Determine the Cartesian components of the electric field and evaluate at the point (+1,0,+2).

9. Over a certain region of space, the electric potential is V = 5r³cos(q )sin²(f ). Determine the spherical components of the electric field and evaluate electric field at the point (r = 1,q = p /2, f = p /4).

10. The potential in a certain region of space is given by V = Ar. Determine the charge density r . Determine the total charge in a sphere of radius R centred at r = 0.

11. In a semiconducting medium, the potential of a charge q is found to be

    

    Find the corresponding electric field and charge density.

Questions? mike.coombes@kwantlen.ca