Relation between field and Potential energy of a body I have read that if a body is in a field and is 
1. moved in a direction opposite to the direction of a field, its potential energy increases.But why does it increase?
2.Also, if we move the body in a direction same as the direction of the field, how will its potential energy be affected.3.If the body is moved in a region where there isn't any field will its potential energy be affected?
 A: First of all, we must be talking about a field that would affect (exert a force on) the object (like a charge in an electric field or an object with mass in a gravitational field).
Now, what does potential energy mean? It is a measure of "stored energy" in the system. That means, if you released it, this energy would be released.


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*Put a book on a shelf and the potential energy is high. You moved it against the gravitational field, which pulls downwards. This namely means that the field can do more work on it, if it is released (if it falls from the shelf). If you only moved it to a shelf at half the height, then gravity can only pull it a shorter distance, if released.

*Take a positive charge and look at the field. It points away from the charge. Now take another positive charge and move it close. It is repelled and pushed away. The closer you move them (you move them against the field), the more they repel. If you let them go they will be pushed away from each other at a higher speed - in other words, moving them closer to each other is the same as storing energy like in a spring that is compressed. 
The more you move an object against a field, the more potential energy is stored, because the field will put more effort into moving the object if released.
If there is no field, then nothing is stored and there is no potential energy difference from one location to another.
A: First, let's pick a field to work with, because particles act differently in different vector fields. Let's say we're dealing with a charged particle in an electrostatic field. 


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*EM fields can be seen as a deformity in spacetime, the field is warping the space in which it is defined. In fact, for advanced EM we use tensors to describe electromagnetic phenomena. As the name suggests, tensors have to do with tension. Originally they were used to describe tension forces on a body (like a beam) but it turns out EM fields act like they are applying tension, so we can model them as such. With that said, moving against the field (not even exactly against, just any component of movement anti-parallel to the field) is a bit like trying to unwind a very heavy sprig: it will tend to shift back.

*Additionally, an electric field can be described as a potential (voltage) difference over a distance. This comes from its units being $\frac {Volts}{meter}$. Also, the work required to move a charged particle in a uniform $E$ field is: $ W = q\Delta V$, where $q$ is the charge on the particle. This can also be rewritten to incorporate $E$ and the distance travelled $d$.
$$ E = \frac{\Delta V}{d} $$
$$ \Delta V = Ed $$
$$ W = qEd $$
So we can see that for a charged particle moving a non-zero distance, if the field strength is uniformly 0 then we have no work done. Conservation of energy would tell us that no work done means no potential gained.
