[Return to Physics Home Page]    [Return to Mike Coombes' Home Page]    [Return to List of Handouts]    [Return to Problem Sets]    [Return to List of Solutions]

Physics 1220 In-Class Problems: Electrostatic Potential

    Potential difference

  1. (a) E = 5x2i. Calculate ΔV between x = 0 m and x = 4 m.

    (b) E = (2/y)j. Calculate ΔV between y = 2 m and y = 5 m.

  2. The electric field between the plates of a capacitor is 1000 V/m and zero everywhere else. The plates are 1.0 mm apart. Put the origin at the positive plate and have the negative plate at x = 1.0 mm. What is the potential difference between x = 0.25 mm and x = 0.75 mm. Which point has the higher potential?

  3. An electric field is given in the diagram below.

    (a) What is V(b) – V(a)?

    (b) What is V(b) – V(c)?

    (c) Find point(s) d so that the V(d) – V(c) = +50.0 Volts.

  4. Find the electrostatic potential difference between points A and B which are distances rA = 1.0 m and rB = 2.0 m from an infinitely long thin wire with λ = 1.0 μC/m. The result E = λ/2πε0r 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 B, what is it's speed at point A?

  5. Find the electrostatic potential between points A and B which are distances xA = 1.0 m and xB = 2.0 m from an infinitely large thin plate with σ = 1.0 μC/m2. The result E = σ/2ε0 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 B, what is it's speed at point A?

  6. The electric field due to a large plate is E = σ/2ε0 as we have seen. A capacitor consists of two identical plates with equal but opposite charge distributions.
    (a) Show that the net electric field is zero outside the plates and Enet = σ/ε0 between the plates.
    (b) Show that the potential difference between the plates is directly proportional to the separation d of the plates.

    7. Potential

  7. An electric field is given by the diagram below where E0 and d are constants. Take V = 0 at x = 0. Find the potential at all points. Plot V versus x.

  8. Repeat the previous problem but take V = 0 at x = ∞.

  9. The electric field due to a uniformly charged long thick plate to be

    where d was the thickness of the plate, ρ0 was the volume charge density, and a is the distance from the centre of the plate. Determine V(x)  where x is the distance from the centre of the plate. Assume V(0) = 0. Plot V as a function of x.

  10. The electric field due to a long thin wire of uniform charge density λ to be E = (λ/2πε0a)r where a is the radial distance from the wire and r is the unit radial vector. Determine V(r) everywhere. Assume V(1) = 0. Plot V as a function of r.

  11. The electric field due to a long thin cylindrical shell of radius R and negative surface charge density σ is

    where the field is radial (i.e. in the r direction). Determine V(r) everywhere. Assume V(0) = 0. Plot V as a function of r.

  12. The electric field due to a solid sphere of radius R and total charge Q to be radial and have the form

    13. where the field is radial (i.e. in the r direction). Determine V(r) relative to V(∞) where r is the distance from the centre of the sphere. Assume V(r=∞) = 0. Plot V as a function of r.

  13. The electric field of a thick spherical shell of total charge Q and inner and outer radii of R and 2R to be

    14. where the field is radial (i.e. in the r direction). Determine V(r) everywhere. Assume V(∞) = 0. Plot V as a function of r.

  14. The electric field due to a thin spherical shell of radius R and surface charge −σ to be

    15. where the field is radial (i.e. in the r direction). Determine V(r) everywhere. Assume V(r=∞) = 0. Plot V as a function of r.

    Point Charges

  15. 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 qf = 1.0 μC and mass M = 15 g has speed vA = 2.50 m/s at point A and it follows the indicated path, what will be its speed at point B?

  16. Five charges are arranged as shown below. What is the electrostatic potential energy of each configuration? The separation between charges is L.

    (a)

    (b)


    Potential Due to a Distribution

  17. A rod is bent into a semi-circular arc of radius R. The rod has a uniform linear charge distribution λ. Find the potential at the centre of the arc, point P. The identity S= Rθ and dS = Rdθ may be of use.

  18. A total charge Q is distributed uniformly along a straight rod of length L. Find the potential at a point P at a distance h from the midpoint of the rod. (Hint: ò[x2+k2]-½dx = ln[x+[x2+k2]½] + C). Use the gradient with respect to h to find the electric field at that point.

  19. Three thin rods of glass of length L carry charges uniformly distributed along their lengths. The charges on the three rods are +Q, +Q, and -Q, respectively. The rods are arranged along the sides of an equilateral triangle. What is the electrostatic potential at the midpoint of this triangle? (Hint: Use the result of the question 20-7.)

    E from V

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

  21. Over a certain region of space, the electric potential is V = 5x-3x2y+2yz2. Determine the components of the electric field and evaluate electric field at the point (1,0,-2).

    22. [Return to Physics Home Page]    [Return to Mike Coombes' Home Page]    [Return to List of Handouts]    [Return to Problem Sets]    [Return to List of Solutions]

    Questions? mike.coombes@kwantlen.ca

    [Return to Kwantlen Homepage]