A,B,C,D are four charges placed at each corner of a square, with A= -6.00 mC , B=6.00 mC, C=-6.00 mC and D=6.00 mC.ALso AB=BC=CD=DA=0.100 m.Determine the magnitude and direction of force on each charge.
Each charge experiences an attraction to the two nearest corners and a repulsion (half as large) from the farthest corner. When the forces from the two nearest corners are added as vectors, the resultant is along the diagonal. When you add up the three forces from the other three corners as vectors, they should cancel out.
To determine the magnitude and direction of the force on each charge, we need to apply Coulomb's Law, which states that the force between two charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them.
Let's go through the process step by step for each charge:
1. Charge A:
- We need to find the net force on charge A due to charges B, C, and D.
- Applying Coulomb's Law, the force on A due to B is given by:
FAB = (k * |Qa| * |Qb|) / r^2, where Qa = -6.00 mC, Qb = 6.00 mC, and r = 0.100 m.
- Since |Qa| and |Qb| are the same magnitude, the force will be attractive, towards B.
- Similarly, the forces due to charges C and D can be calculated using the same formula.
2. Charge B:
- We need to find the net force on charge B due to charges A, C, and D.
- Again, we'll use Coulomb's Law to calculate the forces, similar to step 1.
- The force on B due to A will be attractive towards A, while the forces due to C and D can be calculated in the same manner.
3. Charge C:
- Find the net force on charge C due to charges A, B, and D.
- Apply Coulomb's Law to calculate the forces, similar to the previous steps.
4. Charge D:
- Determine the net force on charge D due to charges A, B, and C.
- Use Coulomb's Law to calculate the forces, similar to previous steps.
By following these steps for each charge and applying Coulomb's Law, you can determine the magnitude and direction of the force on each charge.