A 5.0 µC point charge and a6.0 µC point charge are a distance L apart. Where sho

Question

A 5.0 µC point charge and a6.0 µC point charge are a distanceL apart. Where should a third point charge be placed sothat the electric force on that third charge is zero? I knowthat the third point must be between the other two charges but I donot understand how to calculate how many times L away from the5.0 µC point charge the third pointis. please show how to calculate how many times L away fromthe 5.0 µC point charge the thirdpoint charge should be placed for the electric force on thatthird charge top be zero. thank you

Explanation / Answer

Let        q1 = 5.0C        q2 = q        q3 = 6.0C The force that q1 exerted on q2 is                      F12 = 5.0kq x 10-6 / x2 The force that q2 exerted on q3 is                      F23 = 6.0kq x 10-6 / (L-x)2 Therefore according to condition we have                      F12 = F23                 5.0 x 10-6 / x2 = 6.0 x 10-6/ (L-x)2 ==>     5L2 +5x2 - 10Lx = 6x2 ==>     5L2 - x2- 10Lx = 0 ==>      x2 -5L2 + 10Lx = 0 ==>      x = -5L ± 5.477L

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