Determine the angle through which the moving charge is deflected.

• erisedk
In summary, a particle of mass m and charge q moves at high speed along the x axis from x=-infinity to x=+infinity. As it passes a stationary charge Q fixed at the point x=0, y=-d, the particle acquires a small velocity in the y direction and is deflected at an angle θ from its initial direction of motion. To find this angle, the final vertical component of velocity can be calculated using the definition of ay. Then, using the substitution Ecosθdx and Q/ε in the integral, the value of θ can be found by taking the tangent.
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.

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.

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.

Where should I start?

erisedk said:
Where should I start?
Find the final vertical component of velocity.

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.

Use the definition of ay:

dvy=aydt

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

1. What is the angle of deflection?

The angle of deflection is the amount by which a moving charge is deviated from its original path due to the presence of an external magnetic field.

2. How is the angle of deflection determined?

The angle of deflection is determined by using the equation θ = qBL/mv, where θ is the angle of deflection, q is the charge of the particle, B is the strength of the magnetic field, L is the length of the path traveled by the particle, m is the mass of the particle, and v is its velocity.

3. Can the angle of deflection be negative?

Yes, the angle of deflection can be negative if the moving charge is deflected in the opposite direction of the external magnetic field.

4. Does the angle of deflection depend on the charge of the particle?

Yes, the angle of deflection is directly proportional to the charge of the particle. This means that a particle with a higher charge will experience a greater angle of deflection in the same magnetic field compared to a particle with a lower charge.

5. What factors can affect the angle of deflection?

The angle of deflection can be affected by the strength and direction of the external magnetic field, the charge and mass of the particle, and the velocity and path of the particle.

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