Final answer:
The magnitude of error in Euler approximations is the difference between the approximate values and the exact value. The exact values are implied by E1 being twice the magnitude of E2, and significant figures should be considered when reporting error magnitudes.
Step-by-step explanation:
The student is asking about the magnitude of error in two Euler approximations with different numbers of steps. To find the magnitude of the error in these approximations, we would typically subtract the exact value from the approximate value obtained using Euler's method with 2 and 4 steps, respectively. However, since the exact values are not provided, we are left with the implication that E1 is twice the magnitude of E2 (E1 = 2 * E2). If the true electric field (Etot) is known, we can calculate the errors by subtracting E2 from the actual value for the two-step approximation and E1/2 from the actual value for the four-step approximation. Note that accounting for significant figures is crucial when reporting the magnitude of errors. If the digits retained in a solution are more than the data's significant figures, the calculated magnitude of error should be rounded to match the least number of significant figures among the numbers used in the calculation.