Electric field problem

In summary, the conversation discusses a scenario where a particle with mass m and charge q moves along the x axis at high speed, starting from x=-infinity and ending at x=+infinity. There is also a fixed charge Q at the point x=0, y=-d. As the moving charge passes the stationary charge, it acquires a small velocity in the y direction, but its x component of velocity remains unchanged. The problem at hand is to determine the angle by which the moving charge is deflected, and the conversation ends with a request for help with setting up the integral to solve this problem due to a lack of proficiency in integration.
  • #1
lx2
4
0
A particle of mass m and charge q moves at high speed along x axis. It it 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 charge, its x component of 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.

im quite poor in integration.. any hints, anyone?
 
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  • #2
We need to see some of your work before we can help you -- PF rules. What is the vector force on the moving charge due to the fixed charge, as a function of position? Show us how you set up the integral that you are having trouble with.
 
  • #3


I would approach this problem by using the principles of electromagnetism and the equations that govern the behavior of charged particles in an electric field. Firstly, I would consider the electric field created by the fixed charge Q at the point x=0, y=-d. Using the equation for the electric field, E = kQ/r^2, where k is the Coulomb constant, Q is the charge of the fixed particle, and r is the distance between the two particles, I would calculate the magnitude and direction of the electric field at the position of the moving particle.

Next, I would use the equation for the force experienced by a charged particle in an electric field, F = qE, where q is the charge of the moving particle and E is the electric field, to determine the force acting on the particle in the y direction. Since the velocity of the particle in the x direction is not changing appreciably, the force in the x direction can be neglected.

Using the principles of kinematics, I would then use the equation for the acceleration of a particle, a = F/m, where m is the mass of the particle, to determine the acceleration in the y direction. I would then integrate this acceleration over the time it takes for the particle to travel from x=-infinity to x=+infinity to determine the change in velocity in the y direction.

Finally, I would use trigonometry to calculate the angle through which the particle is deflected, using the change in velocity in the y direction and the initial velocity of the particle in the x direction.

While this problem may involve some challenging mathematical concepts, it is important to remember that as a scientist, it is important to approach problems systematically and use the principles and equations that govern the behavior of the system to find a solution. I would also suggest seeking help from a colleague or mentor who may have a stronger understanding of integration to assist in solving this problem.
 

1. What is an electric field?

An electric field is a physical quantity used to describe the influence that a charged particle has on other charged particles in its surroundings. It is a vector field, meaning it has both magnitude and direction.

2. How is the strength of an electric field measured?

The strength of an electric field is measured in newtons per coulomb (N/C) or volts per meter (V/m). This represents the amount of force exerted on a charged particle (in newtons) per unit of electric charge (in coulombs) or the amount of potential difference (in volts) per unit of distance (in meters).

3. What factors affect the strength of an electric field?

The strength of an electric field is affected by the magnitude of the source charge (the charged particle creating the field), the distance from the source charge, and the medium in which the electric field exists (the type of material or substance surrounding the source charge).

4. How is the direction of an electric field determined?

The direction of an electric field is determined by the direction a positive test charge would move when placed in the field. The direction is always away from a positive source charge and towards a negative source charge.

5. What are some real-world applications of electric fields?

Electric fields have many real-world applications, including powering electronic devices, generating electricity through generators, and controlling the movement of particles in medical equipment such as MRI machines. They are also used in technologies such as capacitors, transformers, and electric motors.

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