Give me the meaning of gauss' law

You are an astronaut, living for a long time interval in the International Space Station (ISS). During your off-duty hours, you have run out of books to read and video games to play. So, your mind wanders to your hobby of music. The last book you read discussed Gauss's law, and you get an inspiration. You plan to attach two nonconducting spheres of radius r = 1.50 cm together using a light insulating string of length L and linear mass density μ = 5.00 x 10-3 kg/m, with the string attached at the surface of each sphere. Then, using the electrical system on the ISS, you will be able to electrify each sphere to a charge of Q = 75.0 μC, uniformly spread over the surface of the sphere. The combination will then be allowed to float freely in the ISS. The spheres will repel, creating a tension in the string. When you pluck the string, you wish it to play a perfect middle C, at 262 Hz. Determine the length of the string (in cm) that you need. (Assume the frequency of 262 Hz is the fundamental…

Problems 4-5 refer to the following diagram and situation. A point charge (with charge Q) at the end of an insulating cord is observed to be in equilibrium in a uniform horizontal electric field of when the pendulum's angle with the vertical is 0 = 38.6°, is as shown in the Figure. The electric field is to the right and the strength of the electric field is 9500 N/C. The mass of the point charge is m = 0.0200 kg and the acceleration due to gravity is 9.8 m/sec². Problem 4: What is the tension on the cord? a. 0.251 N Problem 5: What is the charge Q? a. (1.65 x 10-5)C E b. 0.451 N b. (3.65 x 10-5)C 0 Q m c. 0.651 N C. (5.65 x 10-5) C d. 0.851 N d. (7.65 x 10-5)C

NOTE: This question involves Gauss's Law. I would think one would use the following formula: Φ = qen/ε0. I'm just not sure how to find Φ to solve for qen in Φ = qen/ε0. I'm not given an angle, so I can't use this formula: Φ = EAcosΘ. Help would be appreciated.