Four Wakandan scientists are testing out some new technology that electrically c

Question

Four Wakandan scientists are testing out some new technology that electrically charges any object. Three of the four scientists arrange themselves in an equilateral triangle of side lengthaas shown below, where a= 3 m. They then charge themselves as indicated, where q= 2C. If the fourth scientist charges herself to 4q, where should she stand so that the q scientist experiences no net force?

1. Four Wakandan scientists are testing out some new technology that electrically charges any object Three of the four scientists arrange themselves in an equilateral triangle of side length a as shown below, where a 3 m. They then charge themselves as indicated, where q 2HC (i) If the fourth scientist charges herself to 4q, where should she stand so that the -q scientist experiences no net force?

Explanation / Answer

looking by the symmetry of charges, -q charge will experince forces from 2q ( both up and down) only is x direction, and y component will cancel each other.

Cumulatrive force on -q = 2 K ( +2q) ( +2q) cos 30/ a^2 ...this force is attractive in nature and will be along -x direction, which tells that 4q must be aligned on the right hand side of -q to neutralise this force

2 K ( +2q) (-q) cos 30/ a^2 = K ( 4q) ( -q) / x^2 ( wher x is the distance between 4q and -q)

solving the above expression yields :

cos 30/ a^2 = 1/x^2

plugging teh valuies,

0.866 / 3^2 = 1/x^2

taking sq root on both sides,

x = 1/ 0.31 m = 3.225 m apprx

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