Two charges of +Q are 1 cm apart. If one of the charges is replaced by a charge of -Q, the magnitude of the force between them is

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We start by restating the problem: two charges of +Q are 1 cm apart. If one charge is replaced by -Q, what is the magnitude of the force between them? Options: zero, smaller, the same, larger.

Option 1: zero. This would imply no force acts between the charges. However, any two point charges exert a Coulomb force unless they are infinitely far apart or one of them is zero. Here both charges have nonzero magnitude and finite separation, so a force must exist. Therefore this option is incorrect.

Option 2: smaller. The magnitude of the force between charges depends on the product of the charges and their separation: F = k |q1 q2| / r^2. Replacing +Q with -Q changes the sign of the force (attractive instead of repulsive) but does not change the magnitude, since |(+Q)(-Q)| = Q^2. Thus the force does not become smaller in magnitude; this option is incorrect.

Option 3: the same. This aligns with the Coulomb formula for magnitude, F = k |q1 q2| / r^2. Originally q1 = +Q and q2 = +Q give magnitude k Q^2 / r^2. After replacement, q1 = +Q and q2 = -Q yield magnitude k Q^2 / r^2 as well, since the product in absolute value remains Q^2 and the distance r is unchanged. Therefore, the magnitude remains unchanged. This option is consistent with the physics and is correct.

Option 4: larger. Since the magnitude depends only on the absolute product |q1 q2| and the separation, changing the sign of one charge does not increase the magnitude; it remains the same as long as the separation is the same. Hence this option is incorrect.

In summary, the incorrect choices rely on misconceptions about the magnitude being affected by sign or by assuming a zero or reduced force, while the correct reasoning shows that flipping the sign changes the direction (attraction vs repulsion) but not the magnitude for the given fixed separation.

APPHYSC142-031 with labs Exam Review - Final

Two charges of +Q are 1 cm apart. If one of the charges is replaced by a charge of -Q, the magnitude of the force between them is

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