n infinitely long line of charge has a linear charge density of 5.00×10−12 . A proton is at distance 13.5 from the line and is moving directly toward the line with speed 2900 .

Question

n infinitely long line of charge has a linear charge density of 5.00×10−12 . A proton is at distance 13.5  from the line and is moving directly toward the line with speed 2900 .

jamesj · Answer

2900 m/s ? 

And all that being the case, what is your question?

anonymous · Answer

How close does the proton get to the line of charge?

jamesj · Answer

Ok.  What is the force the proton?

anonymous · Answer

what did you mean ?

jamesj · Answer

What I mean is if we're going to calculate positions or trajectories or energy levels of this proton, we're going to have to understand the force acting on it.

So what is the force acting on this proton?  It is the electric force, F, a vector quantity and it can be written as
$$ F = qE $$ where E is the electric field, also a vector quantity.

Now, what is the electric field on an infinitely long wire with uniform charge density $ \lambda $, as in your problem?

Once we know E we can find F.  Once we know F, we can begin to think about how to use conservation of energy to solve this problem.

anonymous · Answer

E =λ/L

jamesj · Answer

In particular, the overall strategy I would use to solve this problem is this: The electric field does work on the proton.  When the proton has stopped moving, then it is at its closest to the wire.  After that, it starts to accelerate away.  

Now by the Work-Energy Theorem, the work done by the electric force has to go somewhere; in this case it goes into the KE of the particle.  I.e., the particle stops.  Hence the change in KE is 
$$ \Delta KE = -\frac{1}{2}mv^2 $$ where v is the initial velocity.  What we know by the W-E Theorem is that
$$ \Delta KE = \int_{13.5}^x F \cdot dr $$
We want to find x.

Hence we're going to need to have to find an expression for F and then integrate.

jamesj · Answer

No, the electric field can't be a function of the length, because the length L is infinite.  Or do you mean L to be something else?

anonymous · Answer

λ=Q/L

jamesj · Answer

No.  The electric field of an infinite straight wire with linear charge density $ \lambda $ is
$$ E = \frac{\lambda}{2\pi \epsilon_0 r } \hat{r} $$ where $ r $ is the perpendicular distance from the wire and $ \hat{r} $ is the unit vector in the radial direction towards the wire.

jamesj · Answer

Make sense?

anonymous · Answer

sure dude. thanks a lot. Can I ask you a question ?

jamesj · Answer

yes

anonymous · Answer

Are you student ?

jamesj · Answer

No, I studied Physics at university however.

anonymous · Answer

All the best dude. If you want tp pracice more there is a web site www.materingphysics.com I guess it is helpful

jamesj · Answer

interesting

anonymous · Answer

you should buy a code for this to enroll in

anonymous · Answer

sorry this the web http://www.masteringphysics.com/