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Home Minds On Static Electricity Mission SE11 Electric Field Equation Help Help 9

Mission SE11 Electric Field Equation

The Question

The electric field strength at a distance of 2.0 meters from a charged Van de Graaff sphere is 32 N/C. The electric field strength a distance of 0.50 meters from the same sphere is ____ N/C.

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

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. According to the equation, the electric field strength depends inversely on the square of this change. Whatever change is made in d, the inverse change is made in E. And the factor by which the change is made of E is the square of the factor by which the d changes.
 
In this question, the distance is decreased by a factor of four. That is, the new distance is four times smaller than the original distance. Thus, E is increased by a factor of 42. The new electric field strength is sixteen times bigger than the original electric field strength.

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