Placing a charge so that it doesn't move
A positive charge of +3 C and a negative charge of -2 C are 5 m apart, where can you put a charge of +1 C so that it won't move? How do I set up this problem? I know that there are three areas it could be in, but I don't know how to figure out which one.
Answer
First, try drawing a diagram of the situation.:
You're right about having three regions on the line that the charge could go. First, think about a few conceptual questions:
1. Is the force on a positive charge due to a positive charge attractive or repulsive? What about due to a negative charge?
2. Does the force get weaker or stronger the closer the charges are to each other?
3. Does a bigger charge make the force weaker or stronger?
With those concepts in mind, imagine placing the +1 C charge in each region. Try answering the above questions for the force due to each charge on the imaginary +1 C charge. Do the two forces oppose each other, or point in the same direction? If they oppose, will one always win no matter where you place it? Try to determine the location that the forces oppose each other, but can be balanced so as to cancel out. Once you know where it is approximately, use Coulomb's Law for both charges and calculate the position that the forces cancel.
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First, try drawing a diagram of the situation.:
You're right about having three regions on the line that the charge could go. First, think about a few conceptual questions:
1. Is the force on a positive charge due to a positive charge attractive or repulsive? What about due to a negative charge?
2. Does the force get weaker or stronger the closer the charges are to each other?
3. Does a bigger charge make the force weaker or stronger?
With those concepts in mind, imagine placing the +1 C charge in each region. Try answering the above questions for the force due to each charge on the imaginary +1 C charge. Do the two forces oppose each other, or point in the same direction? If they oppose, will one always win no matter where you place it? Try to determine the location that the forces oppose each other, but can be balanced so as to cancel out. Once you know where it is approximately, use Coulomb's Law for both charges and calculate the position that the forces cancel.