A strip of invisible tape 12 cm by 2 cm is charged uniformly with a total net ch

Question

A strip of invisible tape 12 cm by 2 cm is charged uniformly with a total net charge of 4 10-8 coulomb and hangs vertically. You wish to determine the electric field at a perpendicular distance of 3 cm from the center of the tape. Which of the following statements are true? (Select all that apply.)

[ ] Using fewer pieces reduces the error.
[ ] Using more than 8 pieces would make the calculation more accurate.
[ ] Using 3 pieces gives a more accurate result than using 8 pieces.
[ ] It is better to use more, smaller pieces, because each piece is more like a point charge.
[ ] Using more than 8 pieces would not make the calculation more accurate.
[ ] Using 8 pieces gives a more accurate result than using 3 pieces.

And if possible, please explain why. I'm thinking more is better in regards to this answer, but I'm not too sure...

Explanation / Answer

Error in any result is due to two reasons:

(A) Roundoff :

This is caused when we perform multiplication or division of non-integral numbers.

Humans and computers both do roundoff to reach the result.

So when we perform more multiplication / division this error increases.

In our problem if we increase the No. of elements we increase the number of calculations, and hence this error increases.

(B) Error due to Approximation.

This error, as the name implies is due to approximation of a given problem. for example we approximate a diode with ideal diode in first approximation. In our problem, as we decrease the number of elements, approximtion error increases

So, we need to make our approximation, so that its not very crude that approximation-error become large, and also not so fine that the calculation error become too high.

Statement (1): This is not true, since this will increase approximation error too high, since we keep on reducing the numper of pieces.

Statement (2): This is also not true, since in "calculation" , the only error is roundoff. And that will increase with the number of pieces.

Statement (3): This statement is not true, since the distance of observation is near the tape, so this is too crude approximation.

Statement (4) : Not true, calculation error will become too high.

Statement (5): True, Since if we increase the No. of pieces the roundoff error will become dominant.

Statement (6) : True, Since this appears to be neither too crude nor too much calculation involved.

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