(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

In the Bohr Model of a hydrogen atom, a single electron revolves around a single proton in a circle of radius r. Assume that the proton remains at rest.

(a) what is the kinetic energy of the electron?

(b) what is the electrical potential energy?

(c) show that the electron's kinetic energy is equal to half of the electric potential energy.

(give answers in terms ofe, Me, Mp,andr)

2. Relevant equations

KE = 1/2mv^2

F = Ma(centripetal accel.)

a(centripetal accel.) = v^2/r

F = (mv)^2/r = (kqq)/r^2

KE = -1/2U

U = GMm/r^2 = (kqq)/r

v(orbit) = [tex]\sqrt{}GM/r[/tex]

1/2mv^2 = GMm/2r

F = q|E|

|E| = F/q = kq/r^2

3. The attempt at a solution

a)KE = ke^2/2r

b) I am having trouble finding a way to say that KE = -1/2U because I keep getting that...

KE = ke^2/2r

and that

U = GMm/2r even though U should be equal to something like...

U = -GMm/4r

c)cannot find a way to relate them...

----------------------------------------------------------------

1. The problem statement, all variables and given/known data

1. The earth has a net electric charge that causes an electric field at its surface equal to 150N/C and directed inward to the center of the Earth.

(a) What magnitude (and sign) of charge would a 60kg person have to acquire to overcome the weight of the force exerted by the earth's electric field?

(b) What would be the force of repulsion between two people, each with the charge calculated above and separated by 100m?

r = 6.37 x 10^6 m

Me = 5.98 x 10^24 kg

E = 150 N/C

Mp = 60 kg

d = 100m

2. Relevant equations

i) E = f/q = (ma)/q

ii) E = (kq)/r^2

iii) F = q|E| = (kqq)/d^2

3. The attempt at a solution

1a)

using eq. i,

150 = 60(-9.81)/q

q = -3.924 C

1b)

using eq. iii,

F = [(9 x 10^9)(-3.924)^2]/(100)^2

F = 1.39 x 10^7 N

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Electric Fields/potential

**Physics Forums | Science Articles, Homework Help, Discussion**