## Coulomb's Law & Electric Field Problems

 1. Find the net electrical force on the -3.00 nC charge in the following arrangement. The three charges are held on the vertices of a 3-4-5 right triangle as shown. (a) Draw the forces on the -3.00 nC charge. (b) Compute the magnitude of each force. (c) Find the total force; write it in component notation. (d) Find the magnitude and direction of the total force.

2. In the Figure below, a central particle of charge -2q is surrounded by a square array of charged particles, separated by either distance d or d/2 along the perimeter of the square. What are the magnitude and direction of the net electrostatic force on the central particle due to the other particles?

3. Two small spheres with the same mass m=1g have charge Q and 4Q. They are suspended from massless strings of length L=1.00 m. The strings hang making an angle of 20.0º from each other. In this problem you cannot ignore gravity.
(a) What angle does each string make from the vertical?
(b) Determine the charges Q and 4Q.
(c) Sketch what it would look like if both spheres contained charge 2Q. What would 2Q equal?

4. Two Point Charges Assume an x-y coordinate system that is in the horizontal plane, so that we can ignore gravity. Define point A to be at x = -a and point B to be at x = a along the x-axis. Two equal charges of magnitude +Q are held at points A and B. A third charge +q is placed along the y-axis at y=h.
(a) Sketch the set-up as described above.
(b) Compute the total force, magnitude and direction, on charge +q due to the two charges Q, in terms of a, h, Q, q and fundamental constants. Make sure your answer does not include angles or variables that you defined!
(c) Sanity checks: Find the limit for the force as h=0 and for large (but not infinite) h. Do these make sense?
(d) At what height h is the force a maximum? (note, this is messy!!)
(e) Variation: If the two charges along the x axis are of opposite sign, that is, +Q is at A and –Q at B, then what direction is the force on the third charge q at its position x=0, y=h. Why?

5. The magnitude of the gravitational attraction between any two masses m1 and m2 separated by a distance r is given by:
| F g | = G m1 m2 / r2
The gravitational force is responsible for, for example, the orbital motion of planets around the sun.

The magnitude of the electrical repulsion between two like charges q1 and q2 separated by a distance r is given by the Coulomb law:
| F e | = k q1 q2 / r2
The Coulomb force is responsible for, for example, the motion of electrons around the nucleus of an atom.

Consider two protons and recall the constants k and G:

 m = 1.67 x 10-27 kg G = 6.67 x 10-11 N m2 / kg2 q = 1.6 x 10-19 C k = 9 x 109 N m2 / C2

(a) Compute the ratio of the electric force between the two protons to the gravitational force between them at an arbitrary radius r.
(b) Is there any r which will result in a relatively stronger gravitational or electric force?

6. Electric field from two charges Two positive point charges are arranged as shown in the figure below. Q1=16.0 nC and Q2 =4.0 nC. What is the electric field vector at the point P?

7. Two charges located on the x-axis are separated by a distance d. Assume Q1 = 3.00 nC is at the origin, and Q2 = 7.00 nC is10.0 cm to the right. Calculate the location of a charge Q3 be such that the net electric force acting on Q3 is zero.