Electric Potential / Electric Field Question

In summary, the electric potential in a certain region of space is given by V = y^2 + 5xy - 2xyz. The x-, y-, and z-components of the electric field, E, at (5, 2, 3) were determined by taking the partial derivatives with respect to each coordinate and plugging in the given coordinates. The resulting x-, y-, and z-components are Ex = 2, Ey = 1, and Ez = 20. However, these answers may not be accurate due to insufficient significant figures.
  • #1
baillik
5
0
In a certain region of space, the electric potential is given by V = y^2 + 5xy - 2xyz. Determine the x-, y-, and z-components of the electric field, E, at (5, 2, 3). Do not enter units.

I took the partial derivatives with respect to each coordinate:

Ex = -∂V/∂x = -[5y-2yz] = -5y+2yz
Ey = -∂V/∂y = -[2y + 5x - 2xz] = -2y-5x+2xz
Ez = -∂V/∂z = -[-2xy] = 2xy

Then I plugged the coordinates into the equations
Ex = 2
Ey = 1
Ez = 20

These answers are wrong and they don't have enough significant figures either. I am completely lost please help!
 
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  • #2
Well, it's a mystery! The problem gave the x,y,z position to essentially infinite precision, so your answer looks to me to be perfectly acceptable. :confused:
 

1. What is electric potential?

Electric potential, also known as voltage, is a measure of the electric potential energy per unit charge at a given point in an electric field. It is often described as the amount of work needed to move a unit of positive charge from one point to another against an electric field.

2. What is the difference between electric potential and electric field?

Electric potential is a scalar quantity that measures the potential energy of a charge at a specific point in an electric field. On the other hand, electric field is a vector quantity that represents the force per unit charge acting on a charge at a specific point in an electric field.

3. How are electric potential and electric field related?

Electric potential and electric field are closely related, as electric potential is derived from electric field. The electric field at a point is the negative gradient of the electric potential at that point, meaning that it is the rate of change of electric potential with respect to distance.

4. What is the unit of electric potential?

The unit of electric potential is volts (V), which is equivalent to joules per coulomb (J/C). It is named after the Italian physicist Alessandro Volta, who invented the first electric battery.

5. How can electric potential and electric field be measured?

Electric potential can be measured using a voltmeter, which is a device that measures the potential difference between two points in an electric field. Electric field can be measured using an electric field sensor, which measures the strength and direction of the electric field at a given point.

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