Electric Field Strength
Name: Dan F.
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
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
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 ? ****
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
Dr. Ken Mellendorf
Illinois Central College
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Update: June 2012