Three point charges are placed at the following points on the x-axis. 2micro coulomb atbx=0 , -3micro coulomb at x =40cm and -5micro coulomb at x= 120cm calculate the force on -3 micro coulomb charge
To calculate the force on the -3 micro-coulomb charge, we need to calculate the force exerted on it by each of the other charges separately, and then add them up since forces are vector quantities.
The force between two charges can be calculated using 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 step by step:
1. Calculate the force between the -3 micro-coulomb charge and the 2 micro-coulomb charge at x = 0.
The force between these two charges can be calculated using Coulomb's Law as follows:
F1 = k * (q1 * q2) / r^2
where F1 is the force between the charges, k is the electrostatic constant (9 x 10^9 Nm^2/C^2), q1 is the charge of the first charge (-3 micro-coulomb = -3 x 10^-6 C), q2 is the charge of the second charge (2 micro-coulomb = 2 x 10^-6 C), and r is the distance between the charges (in this case 0 cm since they are at the same point on the x-axis).
Plugging in the values, we have:
F1 = (9 x 10^9 Nm^2/C^2) * (-3 x 10^-6 C) * (2 x 10^-6 C) / (0 cm)^2
Note that the force will be repulsive since the charges have opposite signs.
2. Calculate the force between the -3 micro-coulomb charge and the -5 micro-coulomb charge at x = 120 cm.
Similar to step 1, we can use Coulomb's Law to calculate the force between these two charges:
F2 = k * (q1 * q2) / r^2
where F2 is the force between the charges, k is the electrostatic constant, q1 is the charge of the first charge (-3 micro-coulomb), q2 is the charge of the second charge (-5 micro-coulomb = -5 x 10^-6 C), and r is the distance between the charges (120 cm).
Plugging in the values, we have:
F2 = (9 x 10^9 Nm^2/C^2) * (-3 x 10^-6 C) * (-5 x 10^-6 C) / (120 cm)^2
Note that the force will be attractive since the charges have the same sign.
3. Add up the forces to find the net force:
The net force is the vector sum of the forces calculated in steps 1 and 2. Since they are acting in opposite directions, we need to subtract F2 from F1:
Net Force = F1 - F2
Finally, calculate the result using the values calculated in steps 1 and 2.
Keep in mind that all distances should be converted into meters before plugging them into the equations.