# Electric field from potential and coordinate

• axgalloway
In summary, to find the electric field given a potential function V(x,y,z) and point s, you need to take the gradient of the potential function and find the partial derivatives with respect to each variable. Then, use these components to calculate the electric field at the given point.
axgalloway

## Homework Statement

I am given V(x,y,z) = 3x^2 + 2y + 5 and I am given s = (5,3,1), so what is the electric field?

V= Es

## The Attempt at a Solution

I really have no idea. What I tried:

Derivative of V(x,y,z) = 6x+2
so E = 32 N/C?

Really I just don't understand the math necessary. How is it done?

What you really need to do is take the gradient of the potential function:

$$E = - \nabla V$$

You'll find the components of the electric field by taking the partial derivative with respect to each variable. Thus the x-component of the field will be -6x.

Last edited by a moderator:

I would first clarify with the person giving the homework whether they meant electric field or electric potential. The equation given, V(x,y,z) = 3x^2 + 2y + 5, represents the electric potential at a point in space, not the electric field. The electric field is a vector quantity and is given by the equation E = -∇V, where ∇ is the gradient operator. In this case, the electric field would be given by E(x,y,z) = (6x, 2, 0).

To calculate the electric field at the point (5,3,1), we would substitute those values into the equation to get E(5,3,1) = (30, 2, 0) N/C. It is important to note that the units of electric field are Newtons per Coulomb (N/C), not just Newtons (N).

If the homework truly meant to find the electric field from the given potential, then the attempted solution is correct. However, it is important to clarify and understand the concepts and equations involved in order to solve the problem accurately.

## 1. What is an electric field?

An electric field is a force field that surrounds an electrically charged object. It is created by the presence of the charged object and exerts a force on other charged objects within its range.

## 2. How is the electric field related to potential and coordinate?

The electric field is derived from the potential and coordinate of the charged object. The potential, or voltage, is a measure of the electric potential energy per unit charge at a specific point in space. The electric field is the gradient of the potential, meaning it shows the direction and magnitude of the force acting on a charged object at that point.

## 3. What is the equation for electric field from potential and coordinate?

The equation is: E = -∇V, where E is the electric field vector, ∇ is the gradient operator, and V is the potential function.

## 4. How is the direction of the electric field determined?

The direction of the electric field is determined by the direction of the gradient of the potential. It always points in the direction of decreasing potential.

## 5. What is the unit of electric field?

The unit of electric field is Newtons per Coulomb (N/C) in the SI system, or Volts per meter (V/m) in the cgs system.

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