Electric Field - help7

The space surrounding a charged object (source charge) is described as having an electric field. The electric field exerts an electrical influence on other objects that enter that space. The electric field value (E) provides a measure of how strong that influence is. The E value at any given location is dependent upon two factors - the quantity of charge (Q) on the source charge and the distance (R) that the location is from the center of the source charge.

Some problems in Physics don't involve plug-and-chug. They involve the use of an equation as a guide to thinking about how a change in one variable would affect other quantities. That's the case in this question. The variable that is different for these two locations is the distance from the Van de Graaff generator (R vs. 2•R). So you need to use an equation (better known as a relationship) to compare the electric field (E) for these two locations.



The Equation
The relationship between the Electric Field value (E), the separation distance (R) and the quantity of charge (Q) is given by the equation ...

E = k•Q/R²

where k is a proportionality constant.

The Application
From the equation, you would reason that the electric field value (E) is inversely proportional to the square of the separation distance (R). So a larger R value results in a smaller E value. And 2 times the R would result in one-fourth the E value. (The one-fourth is the result of inversing and squaring the 2.) So the location with the two times larger distance will have one-fourth the E value. Put another way, the location with one-half the R value will have a four times larger E value.