A particle of mass and charge enters the region between two horizontal parallel…

PHYSICS · Single correct · AP · Physics 2: Algebra-based · Electric Force Field and Potential · Electric Force Field and Potential

Problem

A particle of mass

m

and charge

q

enters the region between two horizontal parallel plates with initial speed

v_{0}

directed horizontally. The plates have length

L

, and the uniform electric field between them has magnitude

E

directed upward. Gravity acts downward with acceleration

g

. The particle enters exactly halfway between the plates. Which expression gives the particle’s vertical displacement

\Delta y

(upward positive) from its entry point by the time it exits the plates? (a)

\Delta y = \dfrac{\,qE/m + g\,}{2}\,\dfrac{L^{2}}{v_{0}^{2}}

(b)

\Delta y = \dfrac{\,qE/m - g\,}{2}\,\dfrac{L^{2}}{v_{0}^{2}}

(c)

\Delta y = \bigl(\dfrac{qE}{m} - g\bigr)\,\dfrac{L^{2}}{v_{0}^{2}}

(d)

\Delta y = \dfrac{qE}{m}\,\dfrac{L^{2}}{2 v_{0}^{2}}