# Given Electric Potential Function Find where field is zero.

• disfunctlguru
In summary, the electric potential in a certain region is given by V = ax2 + bx + c, where a = 13V/m2, b = -16V/m, and c = 59V. To determine the position where the electric field is zero, the negative gradient of the potential function is taken. After finding that the partials with respect to y and z are zero, the partial with respect to x is found to be Ex = -13x + 16. However, the correct partial derivative is 13x - 16 and taking the opposite of this value gives the function of E. After double checking this derivative, the position where the electric field is zero is found to be approximately 1.23
disfunctlguru
1. The electric potential in a certain region is:
V = ax2 +bx +c

where a = 13V/m2
b = -16V/m
c = 59 V

Determine the postion where the electric field is zero. Answer in units of m.

## Homework Equations

E = -$$\nabla$$V

## The Attempt at a Solution

I know that the Electric Field is the negative gradient of the potential function. I then find that the partials with respect to y and z are zero. Then I find the partial with respect to x is: Ex=-13x+16
Then find the zero to be about 1.23. But it is apparently incorrect. Any help would be appreciated.

disfunctlguru said:
Then I find the partial with respect to x is: Ex=-13x+16
Redo that derivative.

Well the actual partial deriv. is 13x-16. Then I took the opposite to be used as the function of E.

disfunctlguru said:
Well the actual partial deriv. is 13x-16. Then I took the opposite to be used as the function of E.
Double check that.
disfunctlguru said:
1. The electric potential in a certain region is:
V = ax2 +bx +c
What's the derivative of that function?

Thanks, I can't believe I can do some other complex integration etc and mess up a simple deriv... mind blowing.

## 1. What is an electric potential function?

An electric potential function is a mathematical function that describes the electric potential at any point in space due to a given set of electric charges.

## 2. What does it mean for an electric field to be zero?

An electric field is considered to be zero at a certain point when the force exerted on a charged particle at that point is zero. This means that there is no net movement of charged particles at that point.

## 3. How do you find where the electric field is zero given an electric potential function?

To find where the electric field is zero, you can use the equation E = -∇V, where E is the electric field, V is the electric potential function, and ∇ is the gradient operator. Set E equal to zero and solve for the variables to find the points where the electric field is zero.

## 4. What is the significance of finding where the electric field is zero?

Finding where the electric field is zero can help us understand the behavior of charged particles in that region. It can also help us identify points where the electric potential is constant, which can be useful in various applications.

## 5. Can a given electric potential function have multiple points where the electric field is zero?

Yes, a given electric potential function can have multiple points where the electric field is zero. This can happen when the function has multiple local minima or maxima, indicating regions of constant electric potential.

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