# Force due to change in energy

We know change in kinetic energy is equal to total work done by all the forces acting on the object.For work done there should be a force .What's that force.direction?

ex a parallel plate capicitor's dielectric is attached to a mass m which is pulling it downward .We need to find the vale of dielectric so that it stays in it place. The problem is that electric field is horizontal and block is pulling vertical how can we generate a force to prevent dielectric from falling?

• It could be any. What is the context? – Steeven May 24 at 6:52

## 2 Answers

The correct relation is that the change in kinetic energy is equal to the total work done on a particle--not the change in mechanical energy. Or, another relation that holds true is that the work done on a particle by conservative forces is equal to the (negative) of the change in its potential energy.

For example, in a conservative system (i.e., the system where there are only conservative forces), such as an apple falling in the gravitational field of the Earth, the mechanical energy of the apple is conserved--its gain in kinetic energy is balanced in its loss of potential energy. However, the work that is done on the apple (by the gravitational force) is not zero--it is precisely equal to the negative of the change in its potential energy, or, equivalently, equal to the change in its kinetic energy.

Now, the direction of the force acting on a particle for a given change in its kinetic energy could be any. The point is that the work performed by a force on a particle is $$\int\vec{F}\cdot\vec{dr}$$, or, in one dimension, $$\int F dx$$. This means that it not only depends on the force but also depends on the displacement of the particle. Thus, the same amount of work can be done by a force no matter the direction of the force as long as the direction of the displacement of the particle is adjusted correspondingly.

However, if you are only talking about conservative forces, then, by definition, they are given by the (negative) gradient of the potential. So, the direction of a conservative force is given by the direction in which the potential is decreasing the most rapidly. For example, in the case of the gravitational force of the Earth near the Earth-surface, the gravitational potential is given by $$mgh$$. So, it increases with the height $$h$$--so the direction of the gravitational force is towards the decreasing value of $$h$$, i.e., downwards.

• Are you Dvij Mankad? – Unique May 24 at 7:10
• @Unique Lol, that's a bit of doxxing, but yeah. I temporarily changed by ID to respect the demise of the Grumpy Cat. – Dvij Mankad May 24 at 7:12

For a dielectric being pulled into a high-E-field region, one cannot make the usual 'E field is perpenducular to the parallel plates' assumption, because the edge of the dielectric is a fringe region with curved field lines. The polarization of the dielectric makes the separated charges along that edge subject to the external field in the gap versus the (reduced) field inside the dielectric. Because the plates have constant potential (voltage), it means there's a ripple of induced charge in those plates: the capacitor plates' charge is not uniform.

Ignoring 'edge effects' would mean ignoring the force pulling the dielectric into the gap. In physics, that's the wrong thing to do...

So, the problem is NOT well described as 'field is horizontal'. The dielectric has its own charges, and they change the field.