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Problem 52 Medium Difficulty

The current in a wire is defined as the derivative of the charge: $ I(t) = Q'(t) $. (See Example 3.7.3.) What does $ \displaystyle \int^b_a I(t) \, dt $ represent?

Answer

The amount of charge (number of electrons) that pass through an intersection of the wire from time a to time b.

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Video Transcript

remember, in this context, I of tea is equivalent to Q prime of teeth, and we know the integral from A to B of I of T D T is equivalent to being to grow from A to B of Q prime of T D T, which is equivalent to queue of B minus. Q of A. That's the fundamental theme of calculus. So what? This means that this represents the change in amount of the charge from time of a two time of B, so the amount of charge number electrons that pastor intersection of the wire from time to time be.