A positive charge Q is placed at the origin. Four other positive charges are placed on a circle in the x-y plane centered on Q as shown. The top charge is located on the y axis and has a magnitude of 3q. The three bottom charges are symmetric about the y axis as shown and each has magnitude q.

1) Which of the following statements best describes FX, the x component of the net force on the charge at the origin

FX > 0

FX = 0

FX < 0

3) For the collection of charges shown in the above problem, which of the following statements best describes FY, the y component of the net force on the charge at the origin

FY > 0

FY = 0

FY < 0

FX = 0 since the bottom charges are symmetrical about the y axis and the top charge is aligned with the y-axis
3. FY > 0 since the bottom charges do not equate the top charge. The bottom charges have horizontal components which is less than q and adding them all, will not result to 3q.

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snehashish65 snehashish65 · Answer 2 · 2021-11-08T08:01:42-05:00

\(F_{x}=0\) is correct explanation for the net horizontal force on the charge at origin.

\(F_{y}>0\) is correct explanation for the net vertical force on the charge at origin.

Given data:

Magnitude of charge placed at origin is, Q.

The magnitude of charge at y-axis is, 3q.

(1)

Since each charge at y-axis are positive and have magnitude of 3q. Therefore, the force due to charges are at equilibrium. And the horizontal force cannot be greater than zero. Thus, the statement \(F_{x}>0\) is not valid.
The force due to charges 3q and q are at equilibrium. Therefore, the net horizontal force is zero. Thus, \(F_{x}=0\) is the best explanation for the net horizontal force.

Similarly, symmetricity at the bottom also maintains the equilibrium of forces between q and Q. Thus, the statement \(F_{x}<0\) is not valid.

Thus, we conclude that \(F_{x}=0\) is correct explanation for the net horizontal force on the charge at origin.

(3)

Since, the charges at bottom are not equal to the charges at top. The bottom charges have horizontal components of force which is less than q and adding them all, will not result to 3q. Therefore, the net vertical force \(F_{y}\) on Q will be greater than zero. Hence, \(F_{y}>0\) is the best explanation for force on charge at origin.
\(F_{y}=0\) resembles that charges at bottom are equal to charges at top. Which is not true. Hence, the statement is not valid.
Similarly as per the previous explanations, the net force on the charge at origin is greater than zero. But \(F_{y}<0\) resembles the opposite case. Hence, the statement is not valid.

Thus, we conclude that \(F_{y}>0\) is correct explanation for the net vertical force on the charge at origin.

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