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Electricity and Magnetism

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Moderate

Launch Speed of a Charged Particle Towards a Ring of Charge

EANDM-RVWHTJ

Figure 1 shows a ring of charge, with total charge of $q = 39.5 \; \mu \rm{C}$, arrayed on a ring of radius $r = 2.43 \text{ mm}$.

Figure 1. Timothy Black. Created for Albert.io. Copyright 2016. All rights reserved.

If a charged particle of mass $m = 0.472 \text{ g}$ and a charge $q_p = 84.7 \; \mu \rm{C}$ is fired at the ring along the ring axis, from a distance of $l = 7.94 \text{ mm}$, what must be its initial speed $v_0$ so that it can reach the center of the ring?

A

$v_0 = \text{ 7240 m/s}$

B

$v_0 = \text{ 6090 m/s}$

C

$v_0 = \text{ 193 m/s}$

D

$v_0 = \text{ 3920 m/s}$