Determine the angle through which the moving charge is deflected.

[erisedk]

Homework Statement

A Particle of mass m and chargeq oves at high speed along the x axis. It is initially near x=-infinity and it ends up near x=+infinity. A second charge Q is fixed at the point x=0, y=-d. As the moving charge passes the stationary chrge, its x component o velocity does not change appreciably, but it acquires a small velocity in the y direction. Determine the angle through which the moving charge is deflected.

Homework Equations

The Attempt at a Solution

We can't use impulse-momentum or energy equations here. I wrote F = kqQ/d^2 at the origin, dy = 1/2 * kqQ/d^2m * dt^2 where dt is x/v, but I don't know what I'm trying to do, or how I'm going to get there. There's also this thing about considering an infinitely long Gaussian cylinder, but I don't know how that'll fit here.

 

[Nathanael]

Just to make sure no confusion arises, you should say y=-D (because lowercase d is used for differentials).

Why are you trying to integrate dy? Obviously the y-coordinate will keep increasing indefinitely even after the particles are infinitely far (so your integral will diverge and be meaningless).

When they say find the angle it is deflected, they want the angle between the initial direction (the +x-axis) and the final direction of motion.

 

[erisedk]

Where should I start?

 

[Nathanael]

Where should I start?

Find the final vertical component of velocity.

 

[erisedk]

How? I thought of using v^2 = u^2 + 2as since it's a very small time that the force is going to act, but then s (i.e. y) comes in.

 

[Nathanael]

Use the definition of a_y:

dv_y=a_ydt

 

[erisedk]

Got it!
I used what it said to use, substituting in Ecosθdx. 2πd in the integral with Q/ε
Then tanθ = vy/vx