Example 15.2 May the Force Be Zero Goal Apply Coulomb\'s law in one dimension. 2

Question

Example 15.2 May the Force Be Zero Goal Apply Coulomb's law in one dimension. 2.0 m Problem Three charges lie along the x-axis as in Figure 15.7. The positive charge q1 = 16 C is at x = 7 m, and the positive charge q2 = 7 is at the origin. Where must a negative charge q3 be placed on the x-axis so that the resultant electric force on it is zero? 0 2.0 m- Figure 15.7 Three point charges are placed along the x-axis. The charge q3 is negative, whereas q1 and q;2 are positive. If the resultant force on q3 is zero, then the force F 13 exerted by q1 on q3 must be equal in magnitude and opposite the force F 3 exerted by g2 on q3 Strategy If q3 is to the right or left of the other two charges, then the net force on q3 can't be zero, because then F 13 and F23 act in the same direction. Consequently, q3 must lie between the other two charges. Write F 13 and F23 in terms of the unknown coordinate position x, sum them and set them equal to zero, solving for the unknown. The solution can be obtained with the quadratic formula.

Explanation / Answer

force on q3 due to q1:

F31 = k q1 q3 / (7 - x)^2 to the right

force on q3 due to q2:

F32 = k q2 q3 / x^2 to the left

F3 = F31 - F32 = 0

F21= F32

q1 / (7 - x)^2 = q2 / x^2

(7 - x) / x = sqrt(16/7) = 1.512  

x = 2.8 m ........Ans

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now q2 is negative so that point will be left to the q2.

x = - x0

Fnet = k q1 q3 / (x0 + 0.93)^2 - k |q2| q3 / x0^2 = 0

x0 + 0.93 / x0 = sqrt(11.29/1.50) = 2.74

x0 = 0.533

x = - 0.533m ..........Ans

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