Electric field given electric potential

In summary, the electric field strength at a point (1.00 m, 3.00 m) can be found by taking the negative gradient of the electric potential, V = (210x^2 - 170y^2) V, where x and y are in meters. The gradient operator used is \nabla = \frac{\partial}{\partial x} \mathbf{\hat{i}} + \frac{\partial}{\partial y} \mathbf{\hat{j}} +\frac{\partial}{\partial z} \mathbf{\hat{k}}.
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[SOLVED] electric field given electric potential

Homework Statement



The electric potential in a region of space is V = ( 210 x^{2} - 170 y^{2} ) V, where x and y are in meters.

What is the strength of the electric field at ( 1.00 m, 3.00 m ) ?

Homework Equations



E = -dV/ds


The Attempt at a Solution



1. i know i have to find the derivative of the that given equation but i can't figure out where to start...because there are two different variable given...and i don't know in term of which variable i have to find the derivative
 
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  • #2
The E-field is a vector quantity and is given by the negative gradient of the potential.

[tex] \mathbf{E} = -\nabla V [/tex]

the [itex]\nabla[/itex] operator is:

[tex] \nabla = \frac{\partial}{\partial x} \mathbf{\hat{i}} + \frac{\partial}{\partial y} \mathbf{\hat{j}} +\frac{\partial}{\partial z} \mathbf{\hat{k}}[/tex]
 
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  • #3
thank you
 

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

The electric field is the force per unit charge experienced by a stationary point charge in an electric field. The electric potential, on the other hand, is the amount of work required to bring a unit charge from infinity to a particular point in an electric field. The relationship between the two is that the electric field is the negative gradient of the electric potential.

2. How is electric field calculated from electric potential?

To calculate the electric field from electric potential, you can use the formula E = -∇V, where E is the electric field, ∇ is the gradient operator, and V is the electric potential. This means that the electric field is the negative of the gradient of the electric potential.

3. Can electric potential exist without an electric field?

No, electric potential cannot exist without an electric field. Electric potential is a measure of the electric potential energy per unit charge, and this potential energy is created by an electric field. So, wherever there is an electric potential, there must also be an electric field.

4. How is electric potential related to electrical potential energy?

Electric potential is the electrical potential energy per unit charge. This means that the electric potential is a measure of the potential energy that a point charge has due to its position in an electric field. The higher the electric potential, the more potential energy a charge has at that point.

5. Can the electric potential be negative?

Yes, the electric potential can be negative. The sign of the electric potential depends on the direction of the electric field. If the electric field is pointing towards the negative charge, then the electric potential will be negative. If the electric field is pointing towards the positive charge, then the electric potential will be positive.

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