Non-Electrostatic Problem: Closest Distance of Approach

[atavistic]

I encountered a problem which goes like this:

Two charges of mass m and charge q are initially positioned far from each other. Now one is projected towards the other with velocity v . Find the closest distance of approach.

We( in class) solved the problem using energy conservation but I had this doubt later:

Since the charges are moving, the electric field is not static in nature , so how can we define potential of such a field and use it in energy equation? And then I had this another doubt which we encounter more often in gravitation where two masses come towards each other by their mutual attraction, since gravitation is also similar to coulomb's law can we say we cannot gravitational field for a moving body?

 

[ZapperZ]

I encountered a problem which goes like this:

Two charges of mass m and charge q are initially positioned far from each other. Now one is projected towards the other with velocity v . Find the closest distance of approach.

We( in class) solved the problem using energy conservation but I had this doubt later:

Since the charges are moving, the electric field is not static in nature , so how can we define potential of such a field and use it in energy equation? And then I had this another doubt which we encounter more often in gravitation where two masses come towards each other by their mutual attraction, since gravitation is also similar to coulomb's law can we say we cannot gravitational field for a moving body?

Conservation of energy certain works in your first scenario. Think of the harmonic oscillator. The "force" isn't a constant either throughout the motion of the oscillator (eg. mass on a spring). Yet, conservation of energy certainly works there.

The second problem (both masses moving) requires a bit more thought. This is the same problem as the method of images where one has a charge moving towards an infinite conducting plane. There is a difference between this, and moving a charge while keeping the other one fixed. I actually wrote this for a "vexer" contest a while back, so you may want to read this first.

Zz.

 

[atavistic]

I don't think I am satisfied with the harmonic oscillator analogy because there , there is nothing called field .

Awaiting more replies.

 

[ZapperZ]

I don't think I am satisfied with the harmonic oscillator analogy because there , there is nothing called field .

Awaiting more replies.

Er.. the harmonic oscillator potential is used in solid state physics plenty of times. These are the potential field that, to an good approximation, is what holding the crystal lattice in place. Look at the calculation involved in finding the specific heat of a solid.

Besides, what does this matter? A potential field is a potential field! Did you even look at the attached document?

Zz.

 

[Troels]

Since the charges are moving, the electric field is not static in nature , so how can we define potential of such a field and use it in energy equation?

As long as the particle is moving sufficiently "slow" (ie not relativistic) the setup is called "quasistatic" and all the machinery of electrostatics works just fine for all practical purposes.

The situation can be treated exactly by use of retarded potential formulation (or relativistic electrodynamics) but that's hardcore stuff.

And then I had this another doubt which we encounter more often in gravitation where two masses come towards each other by their mutual attraction, since gravitation is also similar to coulomb's law can we say we cannot gravitational field for a moving body?

Technically speaking no. That's why Newtons law of gravity fails to account for more exotic phenomena like black holes. But again, as long as the bodies involved moves sufficiently slow and the mass density is sufficiently low, Newtons law works just fine.

Gravity, in the formulation of general relativity on the other hand, is revealed to behave much like electrodynamic fields, introducing some other field that behaves very similar to a magnetic field