# Relation between E and Potential gradient.

• harjyot
In summary, according to the theory, the relationship between electric potential (E) and potential energy (V) is given by E = -dv/dx or E.dx = -dv. The potential drop should increase if both are positive, but this may seem contradictory when considering the decrease in field strength as distance from a positive charge increases. However, in this situation, the sign of the charge must be taken into account. Similarly, when determining the potential at two points (a and b) along the x-axis, you can simply add or shift the potentials, as they are linear functions. This is because potential can be thought of as the energy required to bring a charge from infinitely far away to the point in question, and the "steep
harjyot
According to the theory,
E= -dv/dx
or E.dx = -dv
So if both are positive, the potential drop should increase.
But as we know, if a positive charge is placed, as the distance from it keeps on increasing, field strength starts decreasing and potential drop should increase But this is contradictory right?

Similarly if we make a diagram of field lines along the x-axis and place a sample charge at (a,0,0) and move it to (b,0,0) such that b>a, how can we predict which is at greater potential : a or b? The field value isn't given

You must take the sign of the charge into account.

UltrafastPED said:
You must take the sign of the charge into account.

Well, yes but Electric Potential is defined in terms of a unit positive charge. The Potential Energy of a charge will depend upon its magnitude and sign.
In situations like this, the thing to do is to follow the signs rigorously and not to trust to intuition. The system is quite consistent.

Isn't that what I said?

I didn't say I disagreed. I was just amplifying and emphasising.

1 person
harjyot said:
So if both are positive, the potential drop should increase.
But as we know, if a positive charge is placed, as the distance from it keeps on increasing, field strength starts decreasing
Yes, this is correct.

harjyot said:
and potential drop should increase
As the field strength decreases the potential drop also decreases. I am not sure why you think otherwise.

harjyot said:
Similarly if we make a diagram of field lines along the x-axis and place a sample charge at (a,0,0) and move it to (b,0,0) such that b>a, how can we predict which is at greater potential : a or b? The field value isn't given
You don't need to calculate fields to determine the potential. Potentials are linear, so you can simply add them up or shift them around like any other linear function.

Think of potential as the energy required to bring a charge from infinitely far away to the point in question. The closer you get to the point in question (say a positive charge), the higher your potential. Now think of the potential as a hilltop. At infinity it is flat, but as you get closer to your charge, the hill gets steeper. This "steepness" is the field.

## 1. What is the relation between E and potential gradient?

The relation between E (electric field) and potential gradient is that the electric field is equal to the negative of the potential gradient. In other words, the electric field is the rate of change of potential per unit distance.

## 2. How is potential gradient calculated?

The potential gradient is calculated by dividing the change in potential (ΔV) by the distance (Δx) over which the potential changes. This can be expressed as ΔV/Δx or dV/dx in calculus notation. The unit of potential gradient is volts per meter (V/m).

## 3. What is the significance of potential gradient in electricity?

Potential gradient is significant in electricity because it determines the strength and direction of the electric field. It is also used to calculate the amount of work done per unit charge in moving a charge from one point to another in an electric field.

## 4. How does potential gradient affect the movement of charges?

Potential gradient affects the movement of charges by exerting a force on them. Charges will move in the direction of decreasing potential, from high potential to low potential. The greater the potential gradient, the stronger the force on the charges and the faster they will move.

## 5. Can potential gradient be negative?

Yes, potential gradient can be negative. This indicates that the potential is decreasing in the direction of the electric field. It is possible for the electric field to be in the opposite direction of the potential gradient, resulting in a negative value.

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