Electric Potential and Coulomb's Law Questions

[dillonmhudson]

Any answers would be great, thanks!

Homework Statement

1. A charge Q is uniformly spread along the x-axis from x=0 to x=l. Find the electric potential function at points on the x-axis for x>l.

2. An electron moves from one point to another where the second point has a larger value of the electric potential by 5 volts. If the initial velocity was zero, how fast will the electron be going at the second point? (The mass of the electron is 9.11E-31 kg)

3. Suppose an electron were moving in a straight line towards a fixed nucleus which had a positive charge 8 times the size of the charge on an electron. If the electron started at infinity with essentially zero velocity, how fast would it be moving when it was 50E-11 m from the nucleus?

Homework Equations

Coulomb's Law = $$\alpha$$*[q1*q2]/r^2
where $$\alpha$$=1/[4*$$\pi$$*$$\epsilon$$$$_{}0$$

U=1/[4*pi*epsilon-sub0]*[q*q sub0]/r

V=U/[q sub0]

The Attempt at a Solution

1. dV=1/[4*pi*epsilon]*[(Q/l)*dx]/[x-l]
dV=1/[4*pi*epsilon]*Q/l
I don't know what to do with this one, the answer has a natural log (ln) in it.

2. KE(initial) + U(initial) = KE(final) + U(final)
0+1/[4*pi*epsilon]*q/r = 1/2 * m * v(final)^2 + 1/[4*pi*epsilon]*q/r
Not sure what to do here either, seem to have three unknowns
Answer = 1.33E6 m/s

3. KE(initial) + U(initial) = KE(final) + U(final)
0=1/2*9.109E-31(mass of an electron)*v(final)^2+9E9*[8*(1.6E-19)^2]/[50E-11]
I don't understand this one eitherThanks for all the help!

 

[Andrew Mason]

Any answers would be great, thanks!

Homework Statement

1. A charge Q is uniformly spread along the x-axis from x=0 to x=l. Find the electric potential function at points on the x-axis for x>l.

2. An electron moves from one point to another where the second point has a larger value of the electric potential by 5 volts. If the initial velocity was zero, how fast will the electron be going at the second point? (The mass of the electron is 9.11E-31 kg)

3. Suppose an electron were moving in a straight line towards a fixed nucleus which had a positive charge 8 times the size of the charge on an electron. If the electron started at infinity with essentially zero velocity, how fast would it be moving when it was 50E-11 m from the nucleus?

Homework Equations

Coulomb's Law = $$\alpha$$*[q1*q2]/r^2
where $$\alpha$$=1/[4*$$\pi$$*$$\epsilon$$$$_{}0$$

U=1/[4*pi*epsilon-sub0]*[q*q sub0]/r

V=U/[q sub0]

The Attempt at a Solution

1. dV=1/[4*pi*epsilon]*[(Q/l)*dx]/[x-l]
dV=1/[4*pi*epsilon]*Q/l
I don't know what to do with this one, the answer has a natural log (ln) in it.

Let s be the position on the x-axis at which the potential is measured. Write out the expression for potential due to the charge element Qdx/l at a position x where $0 \le x \le l$

2. KE(initial) + U(initial) = KE(final) + U(final)
0+1/[4*pi*epsilon]*q/r = 1/2 * m * v(final)^2 + 1/[4*pi*epsilon]*q/r
Not sure what to do here either, seem to have three unknowns
Answer = 1.33E6 m/s

How much kinetic energy does the electron acquire in moving to the second point? (Hint: for a negative charge, the second position is at a lower potential energy per unit negative charge by 5 joules/coulomb).

3. KE(initial) + U(initial) = KE(final) + U(final)
0=1/2*9.109E-31(mass of an electron)*v(final)^2+9E9*[8*(1.6E-19)^2]/[50E-11]
I don't understand this one either

What is the potential energy of the electron at infinity? What is it at the given distance? Where does that potential energy go?

AM

 

[dillonmhudson]

I'm still not getting question 4...

 

[Jebus_Chris]

There is no question 4.

 

[dillonmhudson]

sorry it's 4 in my book, question 1

 

[Jebus_Chris]

The electric potential at point P, along the line, is kq/r d is the distance from the end of the rod to the point.
So...
$$dV = \frac{k}{x}dq$$
$$dq = \lambda dx = Q/L dx$$
$$dV = \frac{kQ}{Lx}dx$$
Then integrate from d to L + d.

 

[dillonmhudson]

Ok thanks! Got it!
I had:
int[k*[(Q/L)dx]/(a-x)] from 0,L

where L is the distance of where the charge is spread

Thanks a lot!