Question

A point charge with charge q1q1 = +5.00 nC is fixed at the origin. A second point charge with charge q2q2 = -6.00 nC is located on the x axis at x = 4.00 m.

1)

Where along the x axis will a third point charge of qq = +2.00 nC charge need to be for the net electric force on it due to the two fixed charges to be equal to zero? (Express your answer to three significant figures.)

37.9 , 45.9 , 41.9, -45.9, are all incorrect

Answer 1

As q1 is positive,q2 is negative and q is again positive so to have net force on q zero the charge q must be placed either to the left of q1(along - X).or to the right of q2(along +X). Also as qq2(12)>qq1(10) and as force is inversely proportional to square of the separation between the two charges concerned, so, charge q must be nearer to q1 as compared to q2. Hence q must be placed to the left of charge q1 that is along - X axis.

Let q be placed at a distance x from charge q1 along negative X axis. Then separation between q and q2 will be (x+4). Now condition for zero net force on charge q is

Force on q due to q1 = Force on q due to q2

Hence from Coulomb's law, we have,

kqq1/x^2 = qq2/(x+4)^2

=> q1/x^2 = q2/(x+4)^2

=> 5×10^-9/x^2 = 6×10^-9/(x+4)^2

=> 5/6 = [x/x+4]^2

=> x/x+4 = 5/6

   => x = (x+4)×0.9128

   => x = 0.9128x + 3.6512

   => x (1-0.9128) = 3.6512

   => 0.0872x = 3.6512

   => x = 3.6512/0.0872

   => x = 41.87 = 41.9

​Ths for net force to be zero on charge q due to the charges q1 and q2, charge q should be placed at

​x = -41.9 m