Question

The nuclei of large atoms, such as uranium, with 9292 protons, can be modeled as spherically symmetric spheres of charge. The radius of the uranium nucleus is approximately 7.4×10−15m7.4×10−15m .

(a) What is the electric field this nucleus produces just outside its surface?
(b) What magnitude of electric field does it produce at the distance of the electrons, which is about 1.0×10−10m m?
(c) The electrons can be modeled as forming a uniform shell of negative charge. What net electric field do they produce at the location of the nucleus?

Answer 1

Part 1
`E = 2.42 * 10^(21) N/C`

Part 2
`E = 1.3 * 10^(13) N/C`

Part 3
`E = 0`

Step-by-step explanation:

Given

Number of protons
`= 92`

Radius of nucleus
`r_n = 7.4 * 10^(-15) m`

Distance of the electrons
`r_1 = 1.0 * 10^ {-10} m`

Part 1

Electric field produced by just outside its surface

`E = (q)/(4\pi*E_0* r_n^2 ) \\E = (9 * 10^ 9 * 92 * 1.6 * 10^(-19))/((7.4* 10^(-15))^2) \\E = 2.42 * 10^(21) N/C`

Part 2

Electric field produced by just outside its surface

`E = (q)/(4\pi*E_0* r_n^2 ) \\E = (9 * 10^ 9 * 92 * 1.6 * 10^(-19))/((1* 10^(-15))^2) \\E = 1.3 * 10^(13) N/C`

Part 3

The net electric field inside a uniform shell of negative charge is zero because the electric flux lines cancel out each other

hence, the solution is

Part 1
`E = 2.42 * 10^(21) N/C`

Part 2
`E = 1.3 * 10^(13) N/C`

Part 3
`E = 0`