Three point charges are placed on the x-axis at x=0, x=10&x=30cm respectively .find the net force on the _2nc charge due to the two other charges?
To find the net force on the -2 nC charge due to the two other charges, we need to consider the electrical forces exerted by each charge individually and then sum them up.
Let's denote the three point charges as q1, q2, and q3, located at x=0 cm, x=10 cm, and x=30 cm respectively.
First, let's calculate the force exerted by q1 on the -2 nC charge. The electrical force between two point charges is given by Coulomb's Law:
F1 = (k * |q1| * |q2|) / r^2
Here, k is the electrostatic constant (9 x 10^9 Nm^2/C^2), |q1| is the magnitude of the charge at x=0 (in this case, q1 = +2 nC), |q2| is the magnitude of the charge at x=10 cm (in this case, q2 = -2 nC), and r is the distance between the charges, which is 10 cm.
Let's calculate F1:
F1 = (9 x 10^9 Nm^2/C^2 * 2 x 10^(-9) C * 2 x 10^(-9) C) / (0.1 m)^2
F1 = (9 x 10^9 Nm^2/C^2 * 4 x 10^(-18) C^2) / 0.01 m^2
F1 = 36 x 10^(-9) N
Next, let's calculate the force exerted by q3 on the -2 nC charge. The formula is the same:
F3 = (k * |q3| * |q2|) / r^2
Here, |q3| is the magnitude of the charge at x=30 cm (in this case, q3 = +2 nC), and r is the distance between the charges, which is 20 cm.
Let's calculate F3:
F3 = (9 x 10^9 Nm^2/C^2 * 2 x 10^(-9) C * 2 x 10^(-9) C) / (0.2 m)^2
F3 = (9 x 10^9 Nm^2/C^2 * 4 x 10^(-18) C^2) / 0.04 m^2
F3 = 9 x 10^(-9) N
Now, to find the net force on the -2 nC charge due to the two other charges, we need to consider the direction and magnitude of each force. Since q1 and q3 have opposite charges, their forces will be attractive and point towards the -2 nC charge. Thus, the force F1 will be in the negative x-direction and F3 will be in the positive x-direction.
To calculate the net force, we need to subtract the magnitudes of the forces since they have opposite directions:
Net force = F3 - F1
Net force = (9 x 10^(-9) N) - (36 x 10^(-9) N)
Net force = -27 x 10^(-9) N
Therefore, the net force on the -2 nC charge due to the two other charges is -27 x 10^(-9) N (in the negative x-direction).