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Home Minds On Static Electricity Mission SE11 Electric Field Equation Help Help 4

Mission SE11 Electric Field Equation

The Question

A charge Q creates an electric field; a test charge q is placed a distance d away in order to measure the strength of the electric field (E) at that location. A doubling of the distance between Q and test charge q would ___.

Formula Fix

The electric field strength (E) at a given location about a source charge is dependent upon the quantity of charge on the source charge (Q) and the distance that the location is from the source (d). The dependency between electric field strength, the quantity of charge on the source charge, and the distance from the source is expressed by the equation
E = k • Q / d2

Don't be Fooled

The electric field strength (E) at a given location about a source is inversely proportional to the square of the distance (d) from that given location. See Formula Frenzy section above. The dependency of electric field strength upon distance follows an inverse square law pattern. The inverse means that an increase in the distance will decrease the electric field strength. The inverse square means that by whatever factor the distance is increased, the electric field strength will be decreased by the square of that factor.

Math Magic

Equations such as the one shown in the Formula Frenzy section are often used as algebraic recipes for problem-solving. But equations can also be powerful guides for thinking about how a variation in one variable would affect another variable. In this question, we have to think about how a variation in d affects the E. The question can be answered by thinking in terms of factors of change. Suppose the distance is increased by a factor of 2. According to the equation, the electric field strength depends inversely on the square of this change. Thus, E is decreased by a factor of 22. Thinking of equations as guides to predicting how one variable affects another variable provides a qualitative feel for relationships.

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