Electric Field - help14

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. This is one of them. This question is all about the inverse square relationship between electric field (E) and separation distance (R). 


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 is proportional to 1/R²

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.) Similarly, 3 times the R value would result in one-ninth the E value. And finally, 4 times the R value would result in one-sixteenth the E value.
 

The Application
In this question, you know the value of E at location X. Location X is on the surface of the sphere and so it is 1•R from the center of the sphere. (That's how we measure distances ... from the location to the center of the charged object ... and not to its surface). Location Y is 3•R from the center of the sphere. And so location Y is three times the distance; the E value at location Y must be one-ninth the E value at location X. So take the value of E at locaton X (given) and divide by 9 to get the answer.