There are two +q charges and two -q charges on the corners of a square of size a. Left upper corner= +q charge, right upper corner= -q charge, left lower corner= -q charge, and right lower corner= +q charge. Compute the net force on each charge.
I know that F= 9x10^9 Nm^2/C^2 x qaxqb/r^2 and that all the charges are attracted to eachother. so would i just find the forces for each charge using that equation, but how do i deal with it pulling in different directions?
For each charge, you have to add the forces due to the three other charges as vectors acting in different directions. Some of the forces are attraction and some are repulsion.
You have the correct formula for the force on each pair of charges.
When you add the forces due to the two adjacent corners, it will be an attraction actng along the diagonal, sqrt2 times larger than the force due to either adjacent corner. The opposite corner will generate a repulsion force in the opposite direction, but lower than the combined effect of the other two forces.
To find the net force on each charge, you need to consider the forces acting on each charge individually and then determine the vector sum of these forces.
Let's consider each charge one by one:
1) Left upper corner (+q charge):
This charge experiences two forces of attraction from the two -q charges. Both forces have the same magnitude but opposite directions since the charges have the same magnitude. The net force acting on the left upper corner charge would be the vector sum of these two forces. Since the charges are placed at diagonally opposite corners, the forces they exert would also be along the diagonals.
2) Right upper corner (-q charge):
Similar to the previous case, this charge also experiences two forces of attraction from the +q charges. Again, the forces have the same magnitude but opposite directions. The net force acting on the right upper corner charge would be the vector sum of these two forces.
3) Left lower corner (-q charge):
This charge also experiences two forces of attraction, one from the +q charge in the left upper corner and the other from the +q charge in the right lower corner. These two forces will add up to give the net force acting on the left lower corner charge.
4) Right lower corner (+q charge):
Finally, this charge experiences two forces of attraction, one from the -q charge in the left upper corner and the other from the -q charge in the right lower corner. The net force acting on the right lower corner charge would be the vector sum of these two forces.
To calculate the magnitude and direction of the net force on each charge, you can use the Coulomb's law equation you mentioned: F = (9 × 10^9 Nm^2/C^2) × (qa × qb) / r^2. Substitute the appropriate values for each charge and their distances to calculate the individual forces. Then, find the vector sum of these forces to get the net force on each charge. Remember that the vector sum must take into account both the magnitude and direction of each force.
Note: If the size of the square (a) and the magnitude of the charges (q) are provided, you can substitute these values in the equation to calculate the forces more accurately.