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Mission SE11 Electric Field Equation

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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 at that location. Which of the following alterations would INCREASE the electric field strength as measured by the test charge q?

Formula Fix

The electric field strength (E) is defined as the amount of force exerted upon a test charge per unit of charge on the test charge (q). That is,
E = F / q.

The electric force (F) depends upon a number of variables as described by Coulomb's law:
Felect= k • Q1• Q2/ d2
 
In the above equation, Q1 might be the source charge Q and Q2 might be the test charge q. If the expression for force as given by the Coulomb's law equation is substituted in for F in the electric field strength equation, then the equation for electric field becomes
E = k • Q / d2

Don't be Fooled

The electric field strength (E) is defined mathematically as the amount of force per charge on the test charge (see first equation in the Formula Frenzy section). This equation may give the false impression that the electric field strength of a source depends on the quantity of charge on the test charge. Don't be fooled! As the quantity of charge on the test charge (q) is increased, the force exerted on it is increased by the same factor. Thus, the ratio of force per charge (F / q) remains the same. Changing the quantity of charge on the test charge will not change the electric field strength. The electric field strength of a source depends on two factors as displayed in the last equation in the Formula Frenzy section.

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