A point charge of 41 mu C is placed at the origin x1 0 of a

A point charge of 4.1 mu C is placed at the origin (x_1 = 0) of a coordinate system, and another charge of -1.9 mu C is placed placed on the x-axis at x_2 = 0.29 m. (a) Where on the x-axis can a third charge be placed in meters so that the net force on it zero? x_3 = ___________ (b) What if both charges are positive: that is, what if the second charge is 1.9 mu C?

Solution

(A) third charge will be put at a point where net field strength due to these two charges will be zero.

that point will be right to x2.

x > x2

{ field strength due to point charge = k q / r^2 }

Enet = [ k(4.1uC) / x^2 ] - [ k (1.9uC) / (x - 0.29)] = 0

(x - 2.9) / x = sqrt(1.9 / 4.1) = 0.68

x = 9.1 m .......Ans

(B) that point will be in between the charges,

0 < x < x2

Enet = [ k (4.1uC) / x] - [ k (1.9uC) / (0.29 - x)] = 0

0.29 - x / x = 0.68

x = 0.17 m