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Question 14 of 36

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SAT Subject Test

The figure shows three large dots representing charges, Q1, P, and Q2, aligned along a straight path such that P is between Q1 and Q2, closer to Q2.

A known positive charge is located at point P that is between two unknown charges, Q subscript 1 end subscript and Q subscript 2 end subscript, as shown above. P is closer to Q subscript 2 end subscript than Q subscript 1 end subscript. If the net electric force acting on the charge at P is zero, it may correctly be concluded that:

Select an Answer

Both Q subscript 1 and Q subscript 2 are positive

Correct Answer: 
No

Both Q subscript 1 and Q subscript 2 are negative

Correct Answer: 
No

Q subscript 1 and Q subscript 2 have opposite signs

Correct Answer: 
No

Q subscript 1 and Q subscript 2 have the same sign, but the magnitude of Q subscript 1 is greater than the magnitude of Q subscript 2

Correct Answer: 
Yes

Q subscript 1 and Q subscript 2 have the same sign, but the magnitude of Q subscript 2 is greater than the magnitude of Q subscript 1

Correct Answer: 
No

The two charges have the same sign, and the magnitude of Q subscript 1 end subscript is greater than that of Q subscript 2 end subscript. For the net force on charge P to be zero, the forces due to the other two charges must act in opposite directions. This means that Q subscript 1 end subscript and Q subscript 2 end subscript can either both attract or both repel charge P, so they are either both negative or both positive, but one cannot determine which. The force between two point charges is proportional to q subscript 1 end subscript q subscript 2 end subscript invisible times divided by r to the power of 2 end exponent, where q subscript 1 end subscript and q subscript 2 end subscript are the magnitudes of the charges and r is the distance between them. Since Q subscript 1 end subscript is farther from point P, it must have a greater magnitude in order to exert a force on P of the same magnitude that Q subscript 2 end subscript does.

Question Difficulty: 
medium