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Name: Dan F.
Status: student
Age: 13
Location: N/A
Country: N/A
Date: 5/15/2003
Question:
Electric Field Strength (E = V/d or -V/d ?). Most website show that E = V/d. For example, one site says, "If you want to move the positive test charge from a position of low to high potential energy, you must do work on the object against the electric field. You would calculate it using...

W = Fd

Remember from before that E = F/q

F =qE

So the change in potential energy of the charged object is W = qEd "

Also, it shows "V = Ed for electric potential in a uniform field."

Here is my inquiry:

According to the A.P. Physics book from Princeton Review, potential difference is defined in terms of an "external force" doing work "against" the Electric Field (W_ext) -not in terms of the work done BY the electric field (W_e = work done BY field).

Potential difference = V = W_ext/q.... and, in fact, A.P. Physics explicitly says that V = W_e/q (Note the negative sign before the W_e.)

Now, the work done BY the electric field would be

W_e = F_e*d, where F_e = electric force exerted BY the electric field = q*E

So, this mean that in terms of work done by an "external force" against the field

W_ext = F_e*q = qEd

In this case, the potential difference would be given by:

V = W_ext/q = qEd/q = Ed

** V = Ed and E = V/d **

The A.P. Physics reference table (from 2001) shows

E_avg = V/d

**** So, WHICH is correct? E = V/d or E = V/d ? ****

Replies:
Dan,

What must be understood is that electric field is a vector. It is not actually a positive or negative number. It is a size, or magnitude, and a direction. The formula E=V/d gives you the size, the magnitude. The sign in E=-V/d is there to tell you that the electric field points in the direction of decrease for electric potential. If moving to the right causes you to experience a larger V, the E points toward the left. "Negative" for a number means less than zero. "Negative" for a vector means opposite direction. Actually, both formulas can be used correctly.

Dr. Ken Mellendorf
Physics Instructor
Illinois Central College


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