Do part (b.) of problem 6 on page 87. Use documentation on the max command to fi

Question

Do part (b.) of problem 6 on page 87. Use documentation on the max command to figure out how to find where the maximum in E occurs, not just the maximum value of E; meaning, at what position in the E vector does its maximum value occur? Using this you can find the position z where that max E occurs. Make a simple x-y plot of electric field intensity (E) versus distance along the ring axis (z). On the plot, create a text box that gives the answer to the problem as "The maximum E of V/m occurs at cm up from the ring" inserting your answers in the blanks. Title the graph. When labeling an axis that has a variable name, symbol and units, the format is similar to that given in these two examples: Velocity, v (m/s) Potential energy, U (J) Label your axes using this format. Upload it as a single page, pdf file in question 9.

Explanation / Answer

For n > 1000, f(n) = n - 4

Let stepf(n) gives total number of steps taken to evaluate f(n).

For n > 1000 this is 1.

Now lets play with few numbers.

f(1001) = 997, stepsf(1001) = 1

f(1000) = f(f(1005)) = f(1001) = 997, stepsf(1000) = 3

f(999) = f(f(1004)) = f(1000) = 997, stepsf(999) = 5

Thus suggests, stepsf(n) = stepsf(n+1) + 2

stepsf(1000) = 3

stepsf(999) = 5

stepsf(998) = 7

So, steps(1000-i) = 3 + i*2

So, stepsf(n) = 2001 + (n-1)*2 = 2n + 1999 for n <= 1000

and stepsf(n) = 1 for n > 1000

and f(n) = 997 for n <= 1000

f(n) = n - 4 for n > 1000

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