At a particular moment, one negative and two positive charges are located as sho

Question

At a particular moment, one negative and two positive charges are located as shown in the figure. Your answers to each part of this problem should be vectors. It helps a great deal to make a diagram with arrows representing the various electric field contributions, and then check the signs of your components against these arrows. Let Q_1 = 1 mu C, Q_2 = 7 mu C, and Q_3 = -6 mu C. Find the electric field at the location of Q_1, due to Q_2 and Q_3. E rightarrow = N/C Use the electric field you calculated in part (a) to find the force on Q_1. F rightarrow = N Find the electric field at location A, due to all three charges. E rightarrow = N/C An alpha particle (He^2+, containing two protons and two neutrons) is released from rest at location A. Use your answer from part (c) to determine the initial acceleration of the alpha particle. (Use 6.646 times 10^-27 kg for the mass of He^2+.) a rightarrow = m/s^2

Explanation / Answer

(a)

formula for electric field due to point charge is

E = kq/r^2

E2= kq2/r^2

= 9 * 10^9 ( 7* 10^-6)/(0.04)^2

=39.37 * 10^6 N/C j

E3 = kq3/r^2 cos thea i - kq3/r^2 sin theta

r = sqrt(0.04)^2 + (0.03)^2 = 0.05

cos theta = 0.03/0.05

sin theta = 0.04/0.05

E3 = 9 * 10^9(6 * 10^-6)/(0.05)^2 (0.03/0.05) i - 9 * 10^9(-6 * 10^-6)/(0.05)^2 (0.04/0.05)

E net = E2 + E3

=12.96 * 10^6 i + 17.28 * 10^3 j - 39.37 * 10^6 j

=12.96 * 10^6 i -22.09 * 10^6 j

E= sqrt( 12.96 * 10^6 )^2+(-22.09 * 10^6)^2 j

= 25.61 * 10^6 N/C

(b)

F = Eq2 = 25.61 * 10^6 N/C * ( 7 * 10^-6) = 179.27 N

(c)

E1 = 9 * 10^9 (1 * 10^-6)/(0.03)^2 = 10* 10^6 i

E2 =  9 * 10^9 (7 * 10^-6)/(0.05)^2 (0.03/0.05) i +  9 * 10^9 (7 * 10^-6)/(0.05)^2 (0.04/0.05) j

=15.12 * 10^6 N/C i + 20.16 * 10^6 N/C j

E3 =-9 * 10^9 ( 6 * 10^-6)/(0.04)^2 j =-33.75 * 10^6 j

E net (A) =25.12 * 10^6 N/C i -13.59 * 10^6 N/C j

E mag = (25.12 * 10^6 N/C )^2+(-13.59 * 10^6 N/C )^2

=28.56 * 10^6 N/C

(d)

F = Eq

ma = Eq

a= Eq/m = 28.56 * 10^6 N/C ( 2 * 1.6 * 10^-19)/6.646 * 10^-27

=13.75 * 10^14 m/s^2

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