1

Although the question stands for itself, I would like to know that if the answer has to be no then does any particular law forbids the existence of such forces; and if there are such forces then what are these and upon travelling under such forces in a closed loop where does the energy come from (as they are non conservative and non dissipative)?

Addendum: I would also highly appreciate it if someone could give an example of force fields which could be set up and left undisturbed by movement of particles under their influence. For example a charged non conducting fixed sphere provides an approximately fixed static field under which if particles move the cause is not disturbed. Since we know about induced electric field, but motion of charged particles under induced electric field, disturb its cause and then we have to supply more energy to maintain the field at original state.

I would hasten to add that although this would be highly appreciated, its not a necessity for the original question.

Qmechanic
  • 220,844
Rijul Gupta
  • 5,589
  • 5
  • 34
  • 59

3 Answers3

2

En electrical field induced by a time-varying magnetic field is non-conservative as $$\nabla \times \vec E =-\frac { \partial \vec B}{\partial t}\neq 0$$ It is impossible to derive a potential function for this field due to the non-vanishing rotor. The work done by the force on a charged particle when moving along a closed trajectory can be non-zero. This is not a violation of the energy conservation, as the varying magnetic field implies that energy is supplied to/drained from the field.

jac
  • 770
0

How about this example: You have a balloon on a tether. During the day it goes up spinning a dynamo connected to a battery, so it produces mechanical work stored as energy in the battery. During the night you reverse the dynamo and pull the balloon back to the ground, but since the balloon is not heated by the sunlight the buoyancy force is smaller at night, so there is a net gain of energy, you can make a solar power plant this way. The buoyancy force in this case is not conservative but there is no dissipation in the system. It all works because of an external source of energy - same as the loop voltage in the secondary winding of a transformer (or in a synchrotron) when you maintain the time-varying magnetic flux dB/dt via an external energy source. In the latter case, the induced electric field would be a non-conservative and non-dissipative force too.

Maxim Umansky
  • 4,415
-1

Yes，there are.For example,magnetic force. Assume a magnet walk in a circle alone the magnetic field line,then we know that magnetic force will do work on it.So it couldn't be a conservative force. Also,the work is positive work, so it's non-dissipative force. So we can see,magnetic force is non dissipative-non conservative force.

user36374
  • 1