Wherever makes the maths easiest - depending on what we want to do.hokhani said:Consider a particle moving near the ground with the ground surface as the zero-point potential reference. If at time t we apply an electric field, say parallel to gravity force, where we should consider as a zero-potential reference point?
Yes - the law of conservation of (total) energy always applies.Does the energy remain conserved (Is the energy equal to that before the time t)?
Thanks. Let us discuss this question more exactly; Suppose that at ##t=0## the particle is at ##h(0)=0## (on the ground) moving with velocity ##v(0)## upwards. According to your proposal we choose the potential reference point at ##h=0##. At ##t=t_1## the particle is at ##h(t_1)=h_1## and we turn on the external electric filed. Just before applying the electric field the total energy is ##E=1/2mv^2(t_1) +h_1## while right after it we have ##E=1/2mv^2(t_1) +h_1+Qh_1## (we consider a positive charge and a downward electric field). So, it seems that the energy is not conserved! I think we should consider the zero point of potential exactly at the point that particle is present there at the time ##t_1##. This way the energy remains conserved.Simon Bridge said:So: to help you think about it, at time t=0, set the gravitational potential and the electric potential at the particle position to be zero.
I think time dependency of potential, forces us to redefine a new potential reference point at ##t=t_1##. Otherwise, energy would not be conserved.Simon Bridge said:What makes you think energy is not conserved?
Right. I have considered the particle as the system, gravitational and electric fields as the external fields. I am only dealing with the system itself so, sources of external fields are not important. It seems that the apparatus doesn't play any role in defining the potential reference.Simon Bridge said:You appear to have excluded the apparatus for turning on the electric field from the systrm.
Beggin the question: what makes you think that this is required at all?hokhani said:I think time dependency of potential, forces us to redefine a new potential reference point at ##t=t_1##. Otherwise, energy would not be conserved.
If you treat only the particle as the system then of course energy for the particle will not be conserved, it does not have to be since the system is not closed wrt to energy.Right. I have considered the particle as the system, gravitational and electric fields as the external fields. I am only dealing with the system itself so, sources of external fields are not important. It seems that the apparatus doesn't play any role in defining the potential reference.
It should be noted that I don't know whether or not energy is conserved in this process. So, I meant that if energy conservation is required (because gravitational and electric fields are conservative forces) it is necessary to redefine the reference point of potential.Simon Bridge said:Beggin the question: what makes you think that this is required at all?
I think this is the main point I should discuss further about. According to your statement, a particle (as a system) with mass m in the gravitational force of the Earth doesn't have conserved energy because we have excluded the earth. Also, energy of an electric charge in an electric field is not conserved if we only consider the charge itself disregarding the external charges that induce the electric field. But the energies of these systems are conserved.If you treat only the particle as the system then of course energy for the particle will not be conserved, it does not have to be since the system is not closed wrt to energy.
Could you please help me with that?What is your question again?
A static gravitational or electric field is "conservative". One of the consequences (or even the definition) is that the work done by the gravitational or electrostatic force on a particle traversing a closed path is zero. If you allow the field to be turned on or off, this will fail to hold in general. That is to say that the work done on a particle as it traverses a closed path (in space) that extends over time need not be zero. Particle accelerators make use of this fact, as do power generation plants.hokhani said:So, I meant that if energy conservation is required (because gravitational and electric fields are conservative forces)
Energy in the total system is always conserved even in the case of non-conservative forces such as friction. In this case, energy is just transferred from one thing to another and the total energy is conserved. I guess that conservation concept is used to provide the possibility of working with a system independent of the generating gears like Earth (in gravitational field) or external charges (which generate electric fields).jbriggs444 said:Energy is still conserved in such a case, but one must consider energy in the total system, including the particle, the field and the generating gear.
A time dependent potential is a mathematical function that describes how a particle's energy changes over time. It takes into account the influence of external forces on the particle, such as electric and magnetic fields.
The time dependent potential affects a particle's motion by changing its energy over time, which in turn affects its velocity and position. This can lead to complex and non-linear trajectories.
Some examples of time dependent potentials include a harmonic oscillator, a Coulomb potential, and a gravitational potential. These potentials can be used to describe the behavior of particles in various physical systems.
Scientists study time dependent potentials by using mathematical models and computer simulations. They also conduct experiments using specialized equipment to measure the effects of these potentials on particles in real-world situations.
Time dependent potentials have various applications in different fields of science, including quantum mechanics, astrophysics, and materials science. They are used to understand the behavior of particles in complex systems and to predict their future motion.