# Mechanical energy conservation

Is the mechanical energy conserved when the speed is constant?

What if we have a charge that entered an electric field due to an external force -which is making a dynamic equilibrium with the electric force- the charge's change in $$\Delta K=0$$ ((no change in speed)), while there is a change in $$\Delta U$$. How is that possible?

• You are saying there is an external force acting on the charge. Can energy be conserved if an external force is doing work on your system? – Aaron Stevens Aug 17 at 8:41
• No. So it is not conserved here. Right? So the work done is equal to the change in PE. – Dana Zamer Aug 17 at 8:43

$$W_{ext}=\Delta E=\Delta K+\Delta U$$

In this case $$\Delta K=0$$, but $$\Delta U\neq0$$.

Therefore the external force is doing work, and $$\Delta E\neq0$$.

Therefore, energy of the system is not conserved.

• Sir it mean potential energy will never be zero ,if there work done on body, because potential energy is itself minus time of work done by conservative force – yuvraj singh Aug 18 at 3:41
• @yuvrajsingh $W_{ext}$ only includes work done by forces that are not taken into account with the potential energy. For example, nonconservative forces. The "ext" means external. I didn't say it represents all forces. Indeed, for the total work all you have is $W=\Delta K$ – Aaron Stevens Aug 18 at 11:18

If you assume that the charge alone is the system then as the net force on the charge is zero no work is done on the charge and so its kinetic energy stays constant - the mechanical energy of the system is conserved as no work is done on the system by an external force.

Electric potential energy is a property of at least two electric charges.
In your example one might consider a system consisting of the charges(s) which produced the electric field through which a charge is being "pushed" by an external force and the charge on which the external force acts.
Here the external force is doing work on the system and as the kinetic energy of the charge has not changed the work done by the external force changes the electrical potential energy of the system of charges - the mechanical energy of the system increases as work is done on the system by an external force.

• True. But there the ME isn't consereved ,right?? – Dana Zamer Aug 17 at 8:46
• @DanaZamer Thanks - True and I have changed my final sentence. – Farcher Aug 17 at 8:51