Equations of Motion for 'Perturbed' Or 'Oblique Incidence' Orbits?

[Physics Enemy]

Hi,

I've been doing a Q where particles undergo circular/near-circular motion in an electric field. The electric field varies as 1/r. With the first particle, they set it off tangentially to the field lines, so it undergoes circular motion.

With the second particle, they set it off at a slight deviation from the tangential line. I figured, also from their diagram, the orbit would look slightly elliptical, perhaps still close to circular.

How do I go about deriving an equation of motion for this 'oblique incidence' particle? My only thoughts at this stage are that the force on the particle varies, since it's radial distance varies, unlike with circular motion.

What does it actually want me to do though?

Thanks!

 

[lippyka]

The equation of motion for this oblique incidence particle can be derived by using Newton's Second Law. This law states that the net force acting on an object is equal to its mass multiplied by its acceleration. Therefore, you can calculate the net force on the particle by taking the derivative of its velocity with respect to time. The electric field will provide a force in the radial direction, and this can be calculated using the equation F = qE, where q is the charge of the particle and E is the electric field. You can then use this to determine the acceleration of the particle, which can then be used to calculate its equation of motion.