Geodesics and Motion in an EM Field

Thread starter Woolyabyss
Start date Apr 19, 2019
Tags

Em Euler lagrange equation Field Geodesics Lagrangian dynamics Motion Special relativity

In summary, a geodesic is the shortest path between two points on a curved surface, following the natural curvature. An electromagnetic field can alter the path of a geodesic by changing the curvature of space-time. Both geodesics and EM fields are important in Einstein's theory of general relativity, which explains how mass and energy can warp space-time. While an object can follow a geodesic without an EM field, its presence can impact the path. These concepts are crucial in understanding the behavior of objects in the universe and have greatly advanced our understanding of it.

Apr 19, 2019

Woolyabyss

Homework Statement: I've attached the problem statement as an image.

Relevant Equations: Euler Lagrange equations

I've also attached my attempt as a pdf file. My main issue seems to be I only get one A partial term. Any help would be appreciated.

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Apr 19, 2019

Woolyabyss

I've just realized my mistake. the partial of q A_b with respect to lambda isn't zero, you get an extra term from the chain rule and it works out nicely.

1. What is a geodesic?

A geodesic is the shortest path between two points on a curved surface, such as the surface of a planet or a black hole. It is the path that follows the curvature of the surface and minimizes the distance traveled.

2. How does an electromagnetic (EM) field affect motion on a geodesic?

An EM field can affect the motion on a geodesic by exerting a force on charged particles. This force can alter the trajectory of the particle, causing it to deviate from its geodesic path.

3. Can an EM field change the shape of a geodesic?

No, an EM field cannot change the shape of a geodesic. The shape of a geodesic is determined by the curvature of the surface it is on, and an EM field does not affect this curvature.

4. How does the mass of an object affect its motion in an EM field?

The mass of an object does not directly affect its motion in an EM field. However, the mass of an object can determine how it responds to the force exerted by the EM field. Objects with a larger mass will experience a smaller acceleration from the same force compared to objects with a smaller mass.

5. Can an object be in a geodesic and an EM field at the same time?

Yes, an object can be in a geodesic and an EM field at the same time. The object will follow its geodesic path while also experiencing the effects of the EM field. This is similar to how an object can be in motion and also experiencing the force of gravity at the same time.