The expressions for e/m and the relative error of e/m due to all of the parameters measured:

(σ ₑ/ₘ) / (e/m) = (σᵥ /V)² + (2 σᵢ /ɪ)² + (2 σʀ /R)² + (2 σᵣ /r)²
Term # 1 2 3 4

Assume your mean measurements of voltage were V-403 ± 1V, current 1-2.35 ± 0.01A, coils radius R-14.4 ± 0.3cm, and curvature of the electron trajectory r = 7.1 ± 0.2cm.
What are the numerical values of each term in the formula of the relative uncertainty above? (HINT: consult Appendix C in your manual.)
Term 1 = .616 × 10^(-5)
Term 2 = 7.24 × 10^(-5)
Term 3 = 174 × 10^(-5)
Term 4 = 317 × 10^(-5)

Look at the numbers above and, assuming that the final relative error needs to be reported as rounded to the nearest integer, make a time saving, intelligent decision on how many terms to keep in your final answer and write the value below. (HINT: values that are smaller by a factor of x10 or more generally will not contribute to the final result.)

Term 1 = (0.616 × 10⁻⁵)

Term 2 = (7.24 × 10⁻⁵)

Term 3 = (174 × 10⁻⁵)

Term 4 = (317 × 10⁻⁵)

(σ ₑ/ₘ) / (e/m) = (499 × 10⁻⁵) to the appropriate significant figures.

Explanation:

(σ ₑ/ₘ) / (e/m) = (σᵥ /V)² + (2 σᵢ/ɪ)² + (2 σʀ /R)² + (2 σᵣ /r)²

mean measurements

Voltage, V = (403 ± 1) V,

σᵥ = 1 V, V = 403 V

Current, I = (2.35 ± 0.01) A

σᵢ = 0.01 A, I = 2.35 A

Coils radius, R = (14.4 ± 0.3) cm

σʀ = 0.3 cm, R = 14.4 cm

Curvature of the electron trajectory, r = (7.1 ± 0.2) cm.

σᵣ = 0.2 cm, r = 7.1 cm

Term 1 = (σᵥ /V)² = (1/403)² = 0.0000061573 = (0.616 × 10⁻⁵)

Term 2 = (2 σᵢ/ɪ)² = (2×0.01/2.35)² = 0.000072431 = (7.24 × 10⁻⁵)

Term 3 = (2 σʀ /R)² = (2×0.3/14.4)² = 0.0017361111 = (174 × 10⁻⁵)

Term 4 = (2 σᵣ /r)² = (2×0.2/7.1)² = 0.0031739734 = (317 × 10⁻⁵)

The relative value of the e/m ratio is a sum of all the calculated terms.

(σ ₑ/ₘ) / (e/m)

= (0.616 + 7.24 + 174 + 317) × 10⁻⁵

= (498.856 × 10⁻⁵)

= (499 × 10⁻⁵) to the appropriate significant figures.

Hope this Helps!!!

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