Taking charge into account when calculating total electric field and potential

[Little Etoile]

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Two charges, +Q and -Q, where Q= 4 x 10 ^-6, separated by d=20cm. Find electric field at point midway between charged.

To get the answer, the book basically makes it E x2, since the E field both point in the same direction. I get this... kinda. But why don't you take charge into account? In other words, if E total= E+ + E-, when you calculate it, the second charge is negative, so why does the book calculate it with it's magnitude instead of its actual charge? Is it because you've already taken into account the negative when you analyzed what direction the electric fields point? In other words, the *actual* formula is: E total= E+ - E-, but because it's a negative minus a negative (since E- has a negative Q), then it becomes E total= E+ + E-? So you can either account for that by knowing both e fields are in the same direction and calculate with the magnitude, or you can just calculate it straight using E total= E+ - E-?

Because in a later problem, you're calculating electric *potential* of a point between two source charges, and at that point you *do* calculate it with the actual charge, rather than the magnitude.

Can someone explain what the difference is?

 

[MeRLin443]

You do take charge into account. Think of a system with a single positive point charge, and picture the field line at 10 cm to the right. You should be picturing a line pointing to the right.

+ --->

Now keep that picture in your head, but at the same time take that picture and flip the axis, that is make the charge negative. The vector direction of the field does not change, nor does it magnitude, only the axis, or side of the point charge, changes.

---> -

Adding these two together gives you --->+---> = ------>.

Hopefully you can see now that the question does not deal with scaler, but vector quantities.