An Electron Is Projected with an Initial Velocity $v _ { 0 } = 8.4 \times 10 ^ { 7 } \mathrm {~m} / \mathrm { s }$

An electron is projected with an initial velocity $v _ { 0 } = 8.4 \times 10 ^ { 7 } \mathrm {~m} / \mathrm { s }$ along the $y$ -axis, which is the centerline between a pair of charged plates, as shown in the figure. The plates are $1.0 \mathrm {~m}$ long and are separated by $0.10 \mathrm {~m}$ . A uniform electric field of magnitude $E$ in the $+ x$ -direction is present between the plates. If the magnitude of the acceleration of the electron is measured to be $8.9 \times 10 ^ { 15 } \mathrm {~m} / \mathrm { s } ^ { 2 }$ , what is the magnitude of the electric field between the plates? $\left( e = 1.6 \times 10 ^ { - 19 } \mathrm { C } \right.$ , $m _ { \text {electron } } = 9.11 \times 10 - 31 \mathrm {~kg}$ )

A) $35,000 \mathrm {~N} / \mathrm { C }$
B) $29,000 \mathrm {~N} / \mathrm { C }$
C) $40,000 \mathrm {~N} / \mathrm { C }$
D) $51,000 \mathrm {~N} / \mathrm { C }$
E) $45,000 \mathrm {~N} / \mathrm { C }$

Correct Answer:

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