Question

An earth-orbiting satellite has a particle beam accelerator used to shoot down enemy ballistic missiles. The accelerator strips the electrons off of hydrogen and accelerates the resulting protons toward earth to hit the missile. The proton beam flows at a rate of 3.0 kg/s. At what rate (C/s) is negative charge accumulating on the satellite?

Answer 1

The satellite is losing positive charge and gaining negative charge at a rate of approximately 2.88 x 10^8 Coulombs per second due to the ejection of protons from the particle beam accelerator.

Step-by-step explanation:

The student is asking about the rate at which negative charge is accumulating on a satellite due to a proton beam. Since each proton has a charge of approximately +1.602 x 10-19 Coulombs, and each hydrogen atom contains one proton, we can determine the charge rate by the rate of protons being shot.

First, we need to find the number of protons in 3.0 kg of hydrogen. The mass of a single proton is approximately 1.67 x 10-27 kg, so the number of protons is 3.0 kg / 1.67 x 10-27 kg/proton, which is about 1.80 x 1027 protons per second.

Since each proton has a charge of +1.602 x 10-19 C, the total charge per second is 1.80 x 1027 protons/s * 1.602 x 10-19 C/proton, resulting in approximately 2.88 x 108 C/s. However, as protons are positive, the satellite is losing positive charge (or gaining negative charge) at this rate.