The figure below shows the electric field lines for two charged particles separa

Question

The figure below shows the electric field lines for two charged particles separated by a small distance. Determine the ratio q_1/q_2. What are the signs of q_1 and q_2? A proton accelerates from rest in a uniform electric field of 580 N/C. At one later moment, its speed is 1.40 Mm/s (nonrelativistic because v is much less than the speed of light). Find the acceleration of the proton. m/s^2 Over what time interval does the proton reach this speed? S How far does it move in this time interval? m What is its kinetic energy at the end of this interval? J

Explanation / Answer

(A) there are 6 lines into q1.

and 18 lines from q2.

q1 / q2 = 6 / 18 = 1/3 Or 0.333

(B) q1 -> negative

q2 -> positive

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(A) a = q E / m

= (1.6 x 10^-19) (580) / (1.673 x 10^-27)

= 5.55 x 10^10 m/s^2

(B) v = u + a t

1.40 x 10^6 = 0 + (5.55 x 10^10)t

t = 2.52 x 10^-5 sec

(C) v^2 - u^2 = 2 a d

(1.40 x 10^6)^2 - 0 = 2(5.55 x 10^10) (d)

d = 17.65 m

(d) KE = m v^2 / 2

= (1.673 x 10^-27) (1.40 x 10^6)^2 / 2

= 1.64 x 10^-15 J

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