1. Electric Force Three positive charges with values 24, 4. and q are arranged a

Question

1. Electric Force Three positive charges with values 24, 4. and q are arranged along the x axis, as shown in the figure. The spacing between the charges is d The charges are labeled 1, 2, and 3 for convenience, as indicated (a) What is the direction of the net force on the charge 2? Why? (b) What is the magnitude of the net force on the charge 2? (c) Suppose a fourth charge of value q/2 is added to the system at a location which makes the net force on charge 2 equal to zero. Where should the fourth charge be placed? (d) Next, assume that the fourth charge is removed and we have the original three charges. Suppose that all 3 charges are suddenly released from the positions shown in the figure. Assuming that all charges have the same mass m, find the acceleration of each of the 3 charges. (Give the magnitude and direction.) 24 3 (e) Now suppose the two charges at the ends are fixed in place at the positions shown in the figure, but the middle charge is allowed to move. There is a location where the net force on the middle charge is zero. Set up an equation which gives the condition for zero net force on the middle charge. (You don't need to solve the equation, just set it up,)

Explanation / Answer

a) towards right.

because, the charge 1 exertes more force than charge 3 on the charge 2.

b) Fnet = |F12| - |F32|

= k*2*q*q/d^2 - k*q*q/d^2

= k*q^2/d^2

c) 4th charge must be placed in between 2nd and 3rd charge.

let x is the distance from 2nd charge where the 4th charge must be placed.

use,

k*q^2/d^2 = k*q*(q/2)/x^2

k*q^2/d^2 = k*q^2/(2*x^2)

==> x = sqrt(d/2)

d) Force on 1st charge, F1 = k*2*q*q/d^2 + k*2*q*q/(2*d)^2

= 2*k*q^2/d^2 + k*q^2/(2*d^2)

= 2.5*k*q^2/d^2

so, a1 = F1/m

= (2.5*k*q^2/d^2)/m

direction : towards -x axis

Force on 2nd charge, F2 = k*2*q*q/d^2 - k*q*q/d^2

= k*q^2/d^2

so, a2 = F2/m

= (k*q^2/d^2)/m

direction : towards +x axis

Force on 3rd charge, F3 = k*2*q*q/(2*d)^2 + k*q*q/d^2

= 1.5*k*q^2/d^2

so, a3 = F3/m

= (1.5*k*q^2/d^2)/m

direction : towards +x axis

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