# a cork has an excess of 5.9 X 1017 e- what is the magnitude of the charge on the cork? If it has an excess of 4.3x1017 p+ what is the magnitude of the charge on the cork? I dont understand how...

a cork has an excess of 5.9 X 1017 e- what is the magnitude of the charge on the cork?

If it has an excess of 4.3x1017 p+ what is the magnitude of the charge on the cork?

I dont understand how these are being asked so I need help.

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### 2 Answers

We must consider two related items with the electric charge:

1. Every body in the neutral state, has the same number of electrons and protons in its structure. The electrification of a body, is due to an excess or a deficiency of electrons. An excess of electrons, results in a negative charge on the body and a deficiency causes a positive charge.

2. The electric charge is quantized. This means that the electron charge is the least amount of electric charge, which may have an electrified body. The electric charge of a body, is always an integer multiple of the charge of the electron (e = 1.602 × 10 -19 C).

a)

Since the electric charge is expressed as a multiple of the charge of the electron e, we have:

Q = ne-, n = 5.9 X 1017 and e- = 1.602 X 10-19 C

Q = (5.9 X 1017) (1.602 X 10-19) = 9.45 X 10-2 C

Q = - 9.45 X 10-2 C

As this is an excess of electrons, the electric charge of the cork, is negative

b)

As only the electrons can move away from the body, then an excess of 4.3x1017 protons, means a deficiency of the same quantity of electrons. The electric charge of the proton is equal and opposite that of the electron, then we have:

Q = np+, n = 4.3 X 1017 and p+ = 1.602 X 10-19 C

Q = (4.3 X 1017) (1.602 X 10-19) = 6.89 X 10-2 C

Q = + 6.89 X 10-2 C

Since this is a deficiency of electrons, the electric charge of the cork, is positive

You need to use the mathematical rule of three, such that:

`6.25*10^18` electrons represent the magnitude of charge of 1 C

`5.9*10^17` electrons represent the magnitude of charge of x C

Evaluating x yields:

`x = (5.9*10^17*1)/(6.25*10^18) => x = 0.0944 C`

**Hence, evaluating the magnitude of the charge of the cork, having the excess of `5.9*10^17` electrons, yields `x = 0.0944 C.` **

Reasoning by analogy, you may evaluate the charge of the cork having an excess of `4.3*10^17` protons, such that:

`x = (4.3*10^17*1)/(6.25*10^18) => x = 0.0688 C`

**Hence, evaluating the magnitude of the charge of the cork, having the excess of `4.3*10^17` protons, yields **`x = 0.0688 C.`