In the figure above there is a particle of charge +4Q at x = 0, and a particle o

Question

In the figure above there is a particle of charge +4Q at x = 0, and a particle of charge + 16Q at x = -3a. Use Q = 2.00 Times 10^-6 C, and a = 40.0 cm. Also, use k = 9.00 Times 10^-9 n m^2 / C^2. At what centimeter mark on the x-axis is the net electric field equal to zero? Calculate the magnitude of the net electric field at x = -2a. Calculate the magnitude of the net electric field at x = +2a. If a particle of charge +3Q was placed at x = +2a, what is the magnitude of the net electric force it would experience?

Explanation / Answer

a) For this condition , Enet=0 to the right of the +4Q charge.

Assume Fnet= 0 a distance ‘r’ from+4Q charge

Enet = E1 + E2

Enet = k16Q/(3a+r)^2   -   k4Q/(r)^2

0 =   (9*10^9*16*2*10^-6)/(3*0.4+r)^2   -   (9*10^9*4*2*10^-6)/(r)^2   

Simplifying gives, r= 1.2 m

b) Enet = E1 + E2

Enet = - k16Q/(a)^2 + k4Q/(2a)^2

Enet = (9*10^9*16*2*10^-6)/(0.4)^2   -   (9*10^9*4*2*10^-6)/(2*0.4)^2   = - 1.7*10^6 N/C

c) Enet = E1 + E2

Enet = - k16Q/(5a)^2 + k4Q/(2a)^2

Enet = -(9*10^9*16*2*10^-6)/(5*0.4)^2 + (9*10^9*4*2*10^-6)/(2*0.4)^2   = 4.05*10^4 N/C

d) Fnet = Enet*3Q = (4.05*10^4 N/C)*(3*2*10^-6) = 0.243 N

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