Electric field from potential V= -x*y^2+z

In summary, the conversation discusses deriving the electric field from the potential function V= -x*y^2+z. The student attempts to solve the problem using the equation V=-∫Eds and makes progress by obtaining the components of the electric field in vector form. However, they are unsure if they are going in the right direction and ask for clarification on the gradient and vector components. The expert then confirms the correct formula for the electric field and reminds the student to include the minus sign in front of the z component.
  • #1
btpolk
38
0

Homework Statement



Derive the electric field for the potential function V= -x*y^2+z


Homework Equations



V=-∫Eds

The Attempt at a Solution



x*y^2-z=∫Eds

d/ds(x*y^2-z)= E*s

(y^2)dx/ds+(2y*x)dy/ds-dzds=E*s

I'm stuck at this point and I'm not really sure if I'm going in the right direction.
 
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  • #2
The electric field is negative gradient of the potential function. Do you know what the gradient is?

ehild
 
  • #3
All I was given is what's in the initial question. Should I just divide the s over and call it a day?
 
  • #4
On the second step what if I multiplied both sides by s then divided by s^2 to get E by itself?
 
  • #5
E is the electric field, and it is a vector, having x, y, z components. You get these components as negative partial derivatives of the potential function.

Ex=-∂V/∂x; Ey=-∂V/∂y; Ez=-∂V/∂z.

ehild
 
  • #6
So in vector form would it be <y^2,2xy,1> = E ?
 
  • #7
There is a minus in front of the z component.

ehild
 

1. What is an electric field?

An electric field is a physical field that surrounds an electrically charged object. It is a force field that affects the movement and behavior of other charged particles within its vicinity.

2. How is electric field strength measured?

Electric field strength is measured in newtons per coulomb (N/C) or volts per meter (V/m). This measures the force exerted on a unit charge placed within the electric field.

3. What is the relationship between electric field and potential?

Electric potential is the amount of work required to move a unit charge from one point to another in an electric field. The strength of the electric field is directly proportional to the electric potential.

4. How does the direction of an electric field relate to the direction of electric potential?

The direction of an electric field is always in the direction in which a positive test charge would move. The direction of electric potential is the direction in which a positive test charge would move to decrease its potential energy.

5. What is the difference between electric potential and electric potential energy?

Electric potential is the amount of potential energy per unit charge at a given point in an electric field. Electric potential energy is the energy that a charged particle has due to its position in an electric field. Electric potential is a scalar quantity, while electric potential energy is a vector quantity.

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