Hello, this is for my Classical Electromagnetism class. I truly don\'t understan

Question

Hello, this is for my Classical Electromagnetism class. I truly don't understand what to do with this question or what is being asked here. I have taken only Physics 1 (Mechanics & Sound) and Physics 2 (Electromagnetism & Optics). Please explain what is being asked, how to respond to the question and explain each step and why it is being done.

1. In this course we will deal primarily with electric interactions. However, there are many similarities to the gravitational interaction. The force due to gravity and the force due to an electric charge both vary like 1/r2, so they will have many other similarities as a result. Most of the calculations we do for the one case will be true for the other. But there are some extremely important differences: (a) Find the value of the electric potential energy of a system consisting of a hydrogen nucleus and an electron separated by the Bohr radius. Find the value of the gravitational potential energy of the same two particles at the same radius. Use the same system of units in both cases. Compare and the contrast the two answers.

Explanation / Answer

Okay, so let's note down all the data required

Mass of proton (nucleus of hydrogen)(m) = 1.67e-27 Kg

Mass of an electron (M) = 9.1e-31 Kg

Charge on electron (Q) = -1.6e-19 C

Charge on proton (q) = 1.6e-19 C

Bohr's radius, r = 0.0529 nm = 0.0529e-9 m

Now, First of all, we will find electric potential energy

U = -kqQ/r

U = -9e0*1.6e-19*1.6e-19 / 0.0529e-9

U = -4.355e-18 J

Similarly, Gravitational potential energy

U' = -GMm / r

Here G is universal gravitational constant and is equal to 6.67e-11 Nm2/kg2

U' = - 6.67e-11*9.1e-31*1.67e-27/0.0529e-9

U' = - 1.916e-57 J

Therefore, if we compare U and U', we can say that gravitational potential energy is around 28 magnitude smaller than electric potential energy.

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