Question

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Electric Force of Three Collinear Points Ranking Task 11 of 25 Constants In the diagram below, there are three collinear point charges: g1, 92, and q3. The distance between gi and g2 is the same as that between g2 and q3. You will be asked to rank the Coulomb force on i due to g2 and q3 Part A Rank the six combinations of electric charges on the basis of the clectric force acting on g1.Define forces pointing to the right as positive and forces pointing to the left as negative. Rank in increasing order by placing the most negative on the left and the most positive on the right. To rank items as equivalent, overlap them. View Available Hint Reset Help

Answer 1

Suppose all 3 charges are +ve, then the force acts in the -ve direction

$F=-q_1\left (\frac{Kq_2}{a^2}+\frac{Kq_3}{4a^2} \right )=-\frac{Kq_1}{a^2}\left ( q_2+\frac{q_3}{4} \right )$

where for simplicity

$K=\frac{1}{4\pi \varepsilon_0}$

So just rank them according to

$F\propto-q_1\left ( q_2+\frac{q_3}{4} \right )$

$(&plus;&plus;&plus;)=(---)<(&plus;&plus;-)=(&plus;-&plus;)<(-&plus;&plus;)=(&plus;--)$