Two charges, -Q and 4Q are a distance L apart. These two charges are free to move but do not because there is a third charge nearby.
1. What must be the magnitude of the third charge and its placement in order for the first two to be in equilibrium?
2. what is the distance = ________________ L from -Q - towards 4 Q
1. What must be the magnitude of the third charge and its placement in order for the first two to be in equilibrium?
2. what is the distance = ________________ L from -Q - towards 4 Q
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The force must be colinear with -Q and + 4Q or they would move sideways.
Prior to introducing the third charge the two are forced in opposite directions. So the force applied by the third charge must also be in an opposite direction. It must be outside the line connecting -Q and +4Q
As the magnitude of the force must be identical and F is proportional to q/R^2 the charge must be twice as far from +4Q as it is from -Q
Therefore the charge must be 2L from +4Q and L from -Q
so it is a distance of -L ( from -Q) if the positive direction is measured from -Q to +4Q
Prior to introducing the third charge the two are forced in opposite directions. So the force applied by the third charge must also be in an opposite direction. It must be outside the line connecting -Q and +4Q
As the magnitude of the force must be identical and F is proportional to q/R^2 the charge must be twice as far from +4Q as it is from -Q
Therefore the charge must be 2L from +4Q and L from -Q
so it is a distance of -L ( from -Q) if the positive direction is measured from -Q to +4Q