A charged body 5microcoulomb is placed along the X-axis at the origin of a coordinate system and a charge -3microcoulomb is placed at (2, 0). Calculate the resultant force in magnitude and direction on charge 6microcoulomb placed at (-2, 0) on the coordinate axis.
To calculate the resultant force on the charge of 6μC, we need to consider the electrostatic force between the charges.
1. Begin by calculating the force between the 5μC and 6μC charges. The formula to calculate the force between two charges is given by Coulomb's Law:
F = (k * |q1 * q2|) / r^2
Where:
F is the force between the charges,
k is the electrostatic constant (k = 8.99 x 10^9 Nm^2/C^2),
q1 and q2 are the magnitudes of the charges, and
r is the distance between the charges.
2. In this case, the charges are placed along the x-axis, so their y-coordinate is 0. Therefore, the distance between the charges, r, is:
r = x2 - x1
r = (-2) - (0)
r = -2
3. Now plug in the values into Coulomb's Law for the force:
F1 = (k * |5μC * 6μC|) / (-2)^2
4. Simplify the expression:
F1 = (8.99 x 10^9 Nm^2/C^2 * 30μC^2) / 4
5. Convert the charge values to coulombs:
F1 = (8.99 x 10^9 Nm^2/C^2 * 3 x 10^-5 C^2) / 4
6. Calculate the force F1:
F1 = 6.747 x 10^4 N
7. Now, calculate the force between the charge at (2, 0) and the charge at (-2, 0) using the same steps:
r = x2 - x1
r = 2 - (-2)
r = 4
8. Calculate the force F2:
F2 = (k * |3μC * 6μC|) / 4^2
9. Simplify the expression:
F2 = (8.99 x 10^9 Nm^2/C^2 * 18μC^2) / 16
10. Convert the charge values to coulombs:
F2 = (8.99 x 10^9 Nm^2/C^2 * 1.8 x 10^-5 C^2) / 16
11. Calculate the force F2:
F2 = 5.6175 x 10^4 N
12. Finally, calculate the resultant force by subtracting the forces:
Resultant force = F2 - F1
= (5.6175 x 10^4 N) - (6.747 x 10^4 N)
= -1.1295 x 10^4 N
The magnitude of the resultant force is 1.1295 x 10^4 N, and the direction is opposite to the positive x-axis.