Homework problems - Electrostatics I

Useful relationships can be found at EQUATIONS.

Force problems

1. Two charges, q1 = +50 uC and q2 = +70 uC, are separated by a distance of 60 cm. Determine the force of repulsion for these charges.

2. Two identical copper spheres are .5 m apart. What should be the (equal) charge on each if the force of repulsion between them is 1 N? How many electrons must be removed from each to accomplish this? If each sphere has a mass of 1 gram, what fraction of the atoms present will lose an electron? What conclusion can you draw from this calculation.

3. Two identical spheres hold the same amount of negative charge. The spheres are fixed a permanent distance apart of 1 m, causing a force of repulsion to be 12 N. A third sphere, identical to the other two but initially uncharged, is brought close at hand. The third sphere touches the first sphere, then the second, and is then removed. Determine the force of repulsion between spheres 1 and 2 now.(Hint: This is an example of charging by conduction. When sphere 3 touches sphere 1, the charges redistribute themselves over the surface of the two spheres in proportion to the area of each.)

4. Three charged bodies lie in a straight line. Body 2 is 1 m to the right of body 1 and both are fixed in place; they cannot move. Body 3 is 1 m to the right of body 2. It is free to move but does not. How are charges 1 & 2 related?

5. Two pith balls ( mass = 1 g each) are suspended from strings 1 m long that are attached to a common point of support. How much (equal) charge is there on each if the force of repulsion causes the strings to be separated by 20 degrees?

Electric Fields

6. Consider two point charges q1 = +5 x 10^-6 C, q2 = -8 x 10^-6 C, separated by a distance of 1 m. a) Find E1 at any point 70 cm from q1. Find E2 at any point 30 cm from q2. What is Enet if these two points are coincident.

7. For the two charges in problem #11, find the place where Enet = 0. What is the significance of a place where Enet = 0?

8. Three identical charges, q = +50uC, are located at the corners of a square 25 cm on the side. Determine the magnitude and direction of the E field at the vacant corner. What is the magnitude and direction of the electric force exerted on a charge of -40 uC now placed at the fourth corner?

9. Revisit problem 4. Given your answer for charges 1 & 2, what is Enet at the site of charge 3?