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Physics/Coulomb's Law and Electric Fields

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Question
Hi, I was just wondering if you would be able to clarify as to why these true and false questions have the answer that is indicated beneath the sentences. These are the only ones left that i do not understand. Thanks for any help, it is greatly appeciated.

1)   Two unequal point charges q_1   and q_2   are held in place separated from each other. A point charge Q  is placed somewhere between them at a point where it remains stationary when released. From this observation, we can conclude that q_1   and q_2 must either both be positive or both be negative.
TRUE

2)   Two nuclei each contain two protons and exert a force 4 N on each other. If we transfer a proton from one of these nuclei to the other, the force on each nucleus is now reduced to 3 N.
TRUE

3)   If two point charges exert a force of 1 N on each other when they are 3 cm apart, they will exert a force of 1/25 N when they are 15 cm apart.
TRUE

4)   It is impossible for any object to have a charge of 7.5 e .
TRUE

5)   If one bag contains a charge 8Q  and another one contains charge Q , the 8Q -bag exerts 8 times as much force on the Q -bag as the Q -bag exerts on the 8Q -bag.
FALSE

Answer
1) In order for the field to be zero at some point between the two fixed charges the two charges must be of the same sign so that the electric field, which is a vector, can cancel out. If the two two charges were of opposite signs their fields would add in the space between them. Remember that electric fields are vector quantities.
2) Since the electrostatic force between two,charges is Fe=k*q1*q2/r*2
The first force would be: F1=k*2*2/r^2=4N
While the second would be: F2=k*1*3/r^2=3n
3) If you increase the distance between the two charges from 3cm to 15cm you are increasing the distance by a factor of five:
Fnew=k*q1*q2/(5*r)^2=Fold/5^2=Fold/25
4) All free charges ever measured have charges that are integer multiples of the charge of an electron. No charge with a charge of 1/2 the charge of an electron has ever been measured.
5) According to Newton's Third Law, for every action there is an equal, but opposite reaction. Therefore, the electrostatic force of q1 on q2 will always be identical in magnitude to the force that q2 exerts on q1.

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James J. Kovalcin

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I am teaching or have taught AP physics B and C [calculus based mechanics & electricity and magnetism] as well as Lab Physics for college bound students. I have a BS in Physics from the University of Pittsburgh and a Master of Arts in Teaching from same. I have been teaching physics for 34 years. I am constantly updating my skills and have a particular interest in modern physics topics.

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