Two charges are fixed on the perimeter of a circular clock face.
+Q is placed at 2 o'clock;
+2Q is at 12 o'clock.
Where should a third charge be placed on the perimeter so that the electric field is zero at the center (point P)?
What relative charge strength is required at that point for the electric field to be zero?
The two contributions must be added vectorially to find the resultant electric field. It appears to put somewhat past 6:30 on the clock.
Resolving into components, observing that each hour on a clockface is separated by 30 degrees:
Horizontal: | Vertical: | |
---|---|---|
+Q | 0.866 left | 0.500 down |
+2Q | --- | 2.000 down |
resultant: | 0.866 left | 2.500 down |
Combining to find the magnitude of the resultant vector yields 2.646 units of electric field at a direction of 19.1 degrees clockwise from 6 o'clock (since the tangent of theta is 0.866/2.500 = 0.346.) This angle corresponds to 38 minutes, 13 seconds past 6 o'clock.
A third charge is to be added on the perimeter to balance the resultant of the two charges above. Since each unit of electric field corresponds to a unit of charge, a charge of 2.646Q will be required.
There are two possibilities for counteracting the other two charges: