Calculate the resultant force at Q3

Question

IF
Q1=-16 μC
distances from Q1 to Q2 is =0.6m
Q2=6 μC
distances from Q1 to Q3 is =0.3m
Q3=-8 μC
In simple steps

Answer 1

To calculate the resultant force at Q3, we need to consider the forces from Q1 and Q2 acting on Q3.

The force between Q1 and Q3 can be calculated using Coulomb's law:

F1 = (k * |Q1 * Q3|) / r1^2

Where k is the electrostatic constant (9 * 10^9 Nm^2/C^2), Q1 and Q3 are the charges (-16 μC and -8 μC respectively), and r1 is the distance between Q1 and Q3 (0.3m).

Substituting the values:

F1 = (9 * 10^9 * |-16 * -8|) / 0.3^2
F1 = (9 * 10^9 * 128) / 0.09
F1 ≈ 1.536 * 10^13 N

The force between Q2 and Q3 can also be calculated using Coulomb's law:

F2 = (k * |Q2 * Q3|) / r2^2

Where Q2 is the charge (6 μC), and r2 is the distance between Q2 and Q3 (0.6m).

Substituting the values:

F2 = (9 * 10^9 * |6 * -8|) / 0.6^2
F2 = (9 * 10^9 * 48) / 0.36
F2 ≈ 1.2 * 10^11 N

To find the resultant force at Q3, we need to calculate the vector sum of F1 and F2:

Resultant force = F1 + F2
Resultant force ≈ 1.536 * 10^13 N + 1.2 * 10^11 N
Resultant force ≈ 1.548 * 10^13 N

Therefore, the resultant force at Q3 is approximately 1.548 * 10^13 N.