Electric Field Question?

I would like to learn how a specific answer (in part B) was derived at.

The problem I'm working on is as follows:

A uranium nucleus has 92 protons. Assume the nucleus to be a point-like charge Q = 92e and ignore interact with other electrons.

A) Determine the magnitude of the E field at a distance of 6.4 x 10^-13 m from the nucleus (about the radius of the innermost electron orbit around the nucleus).

I understand how to complete this part and the relevant equations.

k = 9.0 x 10^9 Nm^2/C^2

E = kq/r^2

e = 1.6 x 10^-19 C

I set up my formula as follows:

(9.0 x 10^9 Nm^2/C^2)(92)(1.6 x 10^-19 C) / (6.4 x 10^-13 m)^2

= 3.2 x 10^17 N/C

B) What is the magnitude of the force exerted on an electron by this E field?

*This is where I'm unsure what to do*

The answer is 5.2 x 10^-2 N, but I'm unsure of how to arrive there based on the information that I have.

1 Answer

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  • 3 months ago
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    The unrounded answer from part a) is 3.2344x10^17 N/C. It's best to use this unrounded value in part b).

    The force on charge q in field E is simply F = qE. We can ignore the electron charge's minus sign as we are only asked for the magnitude of F.

    F = qE

    . .= (1.6x10^-19 C) x (3.2344x10^7 N/C)

    . .= 0.05175N

    Rounded to 2 sig. figs. we can write this as 5.2x10^-2 N.

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