Calculating the electric field from the potential

[paralian]

Homework Statement

What is the magnitude of the electric field at the point (3.00\hat{i} - 2.00\hat{j} + 4.00\hat{k})m if the electric potential is given by V = 2.00xyz^2, where V is in volts and x, y, and z are in meters?

Homework Equations

To calculate the field from the potential, E_{s}=-\delta V/ \delta s (ie E=-dV/ds for each component).

The Attempt at a Solution

E_{x}=-dV_{x}/dx
E_{y}=-dV_{y}/dy
E_{z}=-dV_{z}/dz

I don't know what they mean by 2.00xyz^2.

 

[G01]

I don't know what they mean by 2.00xyz^2.

It is a function describing V. What is actually confusing you about it? Is it that it involves more than one variable?

 

[paralian]

It is a function describing V. What is actually confusing you about it? Is it that it involves more than one variable?

Haha...yes. It's probably something really simple. I just don't know what to do to find each component

 

[G01]

O ok. Maybe it is the concept of the partial derivative that is confusing you?

For instance when you want to find the x component of the field you need to find:

\frac{\partial V}{\partial x}.

In this case, just think of y and z as constants. Similarly, think of x as constant when taking the derivatives with respect to the other variables.

Does this help?

 

[paralian]

O ok. Maybe it is the concept of the partial derivative that is confusing you?

For instance when you want to find the x component of the field you need to find:

\frac{\partial V}{\partial x}.

In this case, just think of y and z as constants. Similarly, think of x as constant when taking the derivatives with respect to the other variables.

Does this help?

2.00yz^2 \frac{\partial x}{\partial x}<br /> =2.00yz^2<br /> =-64

2.00xz^2 \frac{\partial y}{\partial y}<br /> =2.00xz^2<br /> =96

2.00xy \frac{\partial z^2}{\partial z}<br /> =2.00xyz<br /> =-48

\sqrt{64^2 + 96^2 + 48^2}<br /> =125

The answer in the back of the book is 150 N/C.

 

[tiny-tim]

2.00xy \frac{\partial z^2}{\partial z}<br /> =2.00xyz<br /> =-48

\sqrt{64^2 + 96^2 + 48^2}<br /> =125

The answer in the back of the book is 150 N/C.

Hi paralian!

It should be 2.00xy \frac{\partial z^2}{\partial z}<br /> =4.00xyz\,.

That should give you 150.09.