Suppose we have a charge, q_1 = 2 mu C. This charge makes an electric field some
ID: 1838552 • Letter: S
Question
Suppose we have a charge, q_1 = 2 mu C. This charge makes an electric field some distance r = 61 cm away from it. Now suppose our measurement of q_1 is only accurate to within 0.2 mu C, and our measurement of r is only accurate to within 1 cm. If we were to calculate the electric field made by that charge at the indicated distance, what would be the uncertainty in our calculation due only to the uncertainty in the size of q_1? What is the uncertainty in our field calculation due only to the uncertainty in the charge separation r? What is the total uncertainty in our electric field calculation due to the uncertainty in the size of q_1 and the uncertainty in the charge separation r?Explanation / Answer
E = k q / r^2
when considering uncertainty of charge.
E = (9 x 10^9 x (2 +- 0.2) x 10^-6) / (0.61)^2
E = 48374.09 +- 4837.41 N/C
Ans: 4837.41 N/C
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considering uncertainty in distance only.
&E = E sqrt[ 2(&r / r)^2] = 1586.04 N/C
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considering both.
&E = E sqrt[ (&r/r)^2 + (&r/r)^2 + (&q/q)^2]
&E = (48374.09) sqrt[ 2(1/61)^2 + (0.2/2)^2] = 4965.71 N/C