Calculate the magnitude and direction of the Coulomb force on each of the three charges connected in series:
1st - 6 micro Coulombs (positive charge)
2nd - 1.5 micro Coulombs (positive charge)
3dr - 2 micro Coulombs (negative charge)
Distance between 1st and 2nd - 3cm
Distance between 2nd and 3rd - 2cm
We'll first calculate the Coulomb force between 1st and 2nd charges, then between 2nd and 3rd charges.
Coulomb's law states that the force between two charges is given by:
F = k * q1 * q2 / r^2
where F is the force, k is the Coulomb constant (approx. 8.99 * 10^9 N m^2 C^-2), q1 and q2 are the charges, and r is the distance between the charges.
Force between 1st and 2nd charges:
q1 = 6 * 10^-6 C (micro = 10^-6)
q2 = 1.5 * 10^-6 C
r = 3 * 10^-2 m (cm = 10^-2)
F12 = k * q1 * q2 / r^2
F12 = (8.99 * 10^9 N m^2 C^-2) * (6 * 10^-6 C) * (1.5 * 10^-6 C) / (3 * 10^-2 m)^2
F12 ≈ 1.346 N (attractive force, since both charges are positive)
Force between 2nd and 3rd charges:
q1 = 1.5 * 10^-6 C
q2 = -2 * 10^-6 C (negative charge)
r = 2 * 10^-2 m
F23 = k * q1 * q2 / r^2
F23 = (8.99 * 10^9 N m^2 C^-2) * (1.5 * 10^-6 C) * (-2 * 10^-6 C) / (2 * 10^-2 m)^2
F23 ≈ -1.798 N (attractive force, since one charge is positive and the other is negative)
To find the net force on the 2nd charge, we'll use vector addition since the forces act in opposite directions.
F_net = F12 + F23
F_net = 1.346 N + (-1.798 N)
F_net = -0.452 N
The net force on the 2nd charge is 0.452 N in the direction towards the 3rd charge (since it's negative).
The force on the 1st and 3rd charges will be equal in magnitude but opposite in direction to the forces we calculated for the 2nd charge. The 1st charge will experience an attractive force of 1.346 N towards the 2nd charge, while the 3rd charge will experience an attractive force of 1.798 N towards the 2nd charge.
To calculate the magnitude and direction of the Coulomb force on each of the charges, we can use the formula for the Coulomb force:
F = k * (q1 * q2) / r^2
where F is the magnitude of the Coulomb force, k is the Coulomb constant (8.99 x 10^9 Nm^2/C^2), q1 and q2 are the charges, and r is the distance between the charges.
Let's calculate the Coulomb force for each combination of charges:
1. First, let's calculate the Coulomb force between the 1st and 2nd charges.
q1 = 6 micro Coulombs = 6 x 10^-6 C
q2 = 1.5 micro Coulombs = 1.5 x 10^-6 C
r = 3 cm = 3 x 10^-2 m
Plugging the values into the formula, we have:
F(1st-2nd) = (8.99 x 10^9 Nm^2/C^2) * ((6 x 10^-6 C) * (1.5 x 10^-6 C)) / (3 x 10^-2 m)^2
Solving the equation, we get:
F(1st-2nd) ≈ 10.047 N (magnitude)
The direction of the force is attractive since the charges have opposite polarities.
2. Next, let's calculate the Coulomb force between the 2nd and 3rd charges.
q1 = 1.5 micro Coulombs = 1.5 x 10^-6 C
q2 = 2 micro Coulombs = -2 x 10^-6 C (negative charge)
r = 2 cm = 2 x 10^-2 m
Plugging the values into the formula, we have:
F(2nd-3rd) = (8.99 x 10^9 Nm^2/C^2) * ((1.5 x 10^-6 C) * (-2 x 10^-6 C)) / (2 x 10^-2 m)^2
Solving the equation, we get:
F(2nd-3rd) ≈ -56.225 N (magnitude)
The negative sign indicates that the force is repulsive since both charges have the same polarity.
Note: Since the charges are connected in series, the net force on each individual charge is the sum of the forces due to the other charges connected to it.
To calculate the magnitude and direction of the Coulomb force on each of the three charges, we can use Coulomb's law:
F = (k * q1 * q2) / r^2
where F is the magnitude of the force, k is Coulomb's constant (9 x 10^9 Nm^2/C^2), q1 and q2 are the charges, and r is the distance between the charges.
Step 1: Calculate the Coulomb force between the 1st and 2nd charges.
Given:
q1 = 6 micro Coulombs = 6 x 10^-6 C (positive charge)
q2 = 1.5 micro Coulombs = 1.5 x 10^-6 C (positive charge)
r = 3 cm = 3 x 10^-2 m
Using Coulomb's law:
F1-2 = (k * q1 * q2) / r^2
F1-2 = (9 x 10^9 Nm^2/C^2) * (6 x 10^-6 C) * (1.5 x 10^-6 C) / (3 x 10^-2 m)^2
Calculating F1-2:
F1-2 = 4.5 x 10^-3 N
The Coulomb force between the 1st and 2nd charges has a magnitude of 4.5 x 10^-3 N.
Step 2: Calculate the Coulomb force between the 2nd and 3rd charges.
Given:
q2 = 1.5 micro Coulombs = 1.5 x 10^-6 C (positive charge)
q3 = 2 micro Coulombs = 2 x 10^-6 C (negative charge)
r = 2 cm = 2 x 10^-2 m
Using Coulomb's law:
F2-3 = (k * q2 * q3) / r^2
F2-3 = (9 x 10^9 Nm^2/C^2) * (1.5 x 10^-6 C) * (2 x 10^-6 C) / (2 x 10^-2 m)^2
Calculating F2-3:
F2-3 = 6.75 x 10^-3 N
The Coulomb force between the 2nd and 3rd charges has a magnitude of 6.75 x 10^-3 N. Notice that this force is positive, indicating that it is attracting the positive charge towards the negative charge.
Step 3: Sum up the forces to find the total force on each charge.
Since the charges are connected in series, the net force on each charge is the sum of the individual forces acting on it.
For the 1st charge:
The only force acting on the 1st charge is F1-2.
The magnitude of the force is 4.5 x 10^-3 N.
For the 2nd charge:
The forces acting on the 2nd charge are F1-2 and F2-3.
The magnitudes of the forces are 4.5 x 10^-3 N and 6.75 x 10^-3 N, respectively.
To find the total force, we need to add these two forces together:
F2 = F1-2 + F2-3 = 4.5 x 10^-3 N + 6.75 x 10^-3 N = 11.25 x 10^-3 N
For the 3rd charge:
The only force acting on the 3rd charge is F2-3.
The magnitude of the force is 6.75 x 10^-3 N.
So, the net forces on each charge are:
1st charge: 4.5 x 10^-3 N
2nd charge: 11.25 x 10^-3 N
3rd charge: 6.75 x 10^-3 N
Remember that the direction of the force between positive and negative charges is attractive, while the force between like charges (positive-positive or negative-negative) is repulsive.