Suppose you want to neutralize the gravitational attraction between the earth and the moon by placing equal amounts of charge on each. (a) Should the charges be both positive, both negative, or one positive and the other negative? Why? (b) Do you need to know the distance between the earth and the moon to find the magnitude of the charge? Why or why not? The masses of the earth and moon are

$$5.98 \times 10 ^ { 24 }$$

and

$$7.35 \times 10 ^ { 22 } \mathrm { kg }$$

respectively. Identical amounts of charge are placed on each body, such that the net force (gravitational plus electrical) on each is zero. What is the magnitude of the charge?

(a) If the masses of Earth and the Moon were both doubled, by how much would the radius of the Moon’s orbit about Earth have to change if its speed did not change? (b) By how much would its speed have to change if its radius did not change? Justify each answer.

Three point charges are fixed to the corners of a square, one to a corner, in such a way that the net electric field at the empty corner is zero. Do these charges all have (a) the same sign and (b) the same magnitude (but, possibly, different signs)?

Suppose Earth and the Moon each carried a net negative charge −Q. Approximate both bodies as point masses and point charges. (a) What value of Q is required to balance the gravitational attraction between Earth and the Moon? (b) Does the distance between Earth and the Moon affect your answer? Explain. (c) How many electrons would be needed to produce this charge?

A charge of

$$- 3.00 \mu \mathrm { C }$$

is fixed at the center of a compass. Two additional charges are fixed on the circle of the compass (radius = 0.100 m). The charges on the circle are

$$- 4.00 \mu \mathrm { C }$$

at the position due north and

$$+ 5.00 \mu \mathrm { C }$$

at the position due east. What is the magnitude and direction of the net electrostatic force acting on the charge at the center? Specify the direction relative to due east.