Three point charges, q1, q2, and q3, lie along the x-axis at x=0, x=3 cm, and x=5 cm, respectively. Calculate the magnitude and direction of the electric force on each of the three points when q1=+6.0 muC, q2=+1.5 muC, and q3=-2.0 muC.
I would add the forces. Watch direction. Draw a figure, label the directions (like charges repel, unlike attract) at each point. That way, you wont get the signs wrong.
Example: at q2, the right charge pulls the q2 to right (call that positive), and the left charge repels it to the right (again positive) so in this case the forces add to the right.
p00p
Three point charges, q 1 , q 2 , and q 3 , lie along the x-axis at x = 0, x = 3.0 cm, and x = 5.0 cm, respectively. Calculate the magnitude and direction of the electric force on each of the three point charges when q 1= +6.0 μC, q 2= +1.5 μC, and q 3= −2.0 μC.
69 hehe
To calculate the magnitude and direction of the electric force on each point charge, we can use the formula for the electric force between point charges:
F = k * |q1 * q2| / r^2
where F is the magnitude of the force, k is the electrostatic constant, q1 and q2 are the magnitudes of the charges, and r is the distance between the charges.
First, let's calculate the force on q1 when q2 and q3 are present. The distance between q1 and q2 is 3 cm, and the distance between q1 and q3 is 5 cm.
F1 = k * |q1 * q2| / r1^2
F1 = (9 * 10^9 N*m^2/C^2) * |(6.0 * 10^-6 C) * (1.5 * 10^-6 C)| / (0.03 m)^2
F1 = (9 * 10^9 N*m^2/C^2) * (9 * 10^-12 C^2) / 0.0009 m^2
F1 = 9 * 10^-3 N
The direction of the force on q1 will be in the positive x-direction.
Next, let's calculate the force on q2 when q1 and q3 are present. The distance between q2 and q1 is also 3 cm, and the distance between q2 and q3 is 2 cm.
F2 = k * |q2 * q1| / r2^2 + k * |q2 * q3| / r3^2
F2 = (9 * 10^9 N*m^2/C^2) * |(1.5 * 10^-6 C) * (6.0 * 10^-6 C)| / (0.03 m)^2 + (9 * 10^9 N*m^2/C^2) * |(1.5 * 10^-6 C) * (-2.0 * 10^-6 C)| / (0.02 m)^2
F2 = (9 * 10^9 N*m^2/C^2) * (9 * 10^-12 C^2) / 0.0009 m^2 + (9 * 10^9 N*m^2/C^2) * (3 * 10^-12 C^2) / 0.0004 m^2
F2 = 9 * 10^-3 N + 67.5 * 10^-3 N
F2 = 76.5 * 10^-3 N
The direction of the force on q2 will be in the positive x-direction.
Lastly, let's calculate the force on q3 when q1 and q2 are present. The distance between q3 and q1 is 5 cm, and the distance between q3 and q2 is 2 cm.
F3 = k * |q3 * q1| / r4^2 + k * |q3 * q2| / r5^2
F3 = (9 * 10^9 N*m^2/C^2) * |(-2.0 * 10^-6 C) * (6.0 * 10^-6 C)| / (0.05 m)^2 + (9 * 10^9 N*m^2/C^2) * |(-2.0 * 10^-6 C) * (1.5 * 10^-6 C)| / (0.02 m)^2
F3 = (9 * 10^9 N*m^2/C^2) * (12 * 10^-12 C^2) / 0.0025 m^2 + (9 * 10^9 N*m^2/C^2) * (3 * 10^-12 C^2) / 0.0004 m^2
F3 = 43.2 * 10^-3 N + 67.5 * 10^-3 N
F3 = 110.7 * 10^-3 N
The direction of the force on q3 will be in the negative x-direction.
In summary:
- The magnitude and direction of the electric force on q1 is 9 * 10^-3 N in the positive x-direction.
- The magnitude and direction of the electric force on q2 is 76.5 * 10^-3 N in the positive x-direction.
- The magnitude and direction of the electric force on q3 is 110.7 * 10^-3 N in the negative x-direction.