Given:
The charge on sphere A, q_A=6.40×10⁻⁶ C
The charge on sphere B, q_B=6.51×10⁻⁶ C
The charge on sphere C, q_C=2.12×10⁻⁶ C
The distance between charge A and B, d_B=0.417 m
The distance between charge A and C, d_C=0.301 m
To find:
a. Magnitude of force between A and B.
b. The magnitude of the force between A and C.
c. The net force on A.
d. The magnitude of the electric field at A.
Step-by-step explanation:
The force between two charges is given by,

Where k is the coulomb's constant, q₁ and q₂ are the charges and d is the distance between the two charges.
a.
The force between A and B is,

b.
The force between A and C is,

c.
The forces when represented in the vector form,

Where i_cap and j_cap are the unit vectors along the negative x-axis and negative y-axis respectively.
The net force acting on sphere A is,

On substituting the known values,

The magnitude of the net force is given by,

d.
The electric field at point A due to charge B is

On substituting the known values,

The electric field at point A due to charge C is

On substituting the known values,

The electric field at point A due to sphere A is zero ans the distance from sphere A to point A is zero
Thus the net electric field at point A is given by,

The magnitude of the net electric at point A is,

Step-by-step explanation:
a. The magnitude of the force exerted on sphere A by sphere B is 2.16 N
b. The magnitude of the force exerted on sphere A by sphere C is 1.35 N
c. The magnitude of the net force on sphere A is 2.55 N
c. The magnitude of the net electric field at point A is 397.3×10³ N/C