Three charges are arranged in a line. From left to right, the charges are:
Q1= -8mC, Q2 = +3mC and Q3 = -4mC. The distance between Q1 and Q2 is 0.3 m, and the distance between Q2 and Q3 is 0.2 m. Calculate the net electrostatic force on Q3.
how can you find what point Q2 will be at equilibrium. show work
the point where Q2 will be at equilibrium?
The forces on each side are equal and opposite.
Now Q1 is neg, Q2 is positive, so the force on Q2 will be to the left. But Q2 is +, and Q3 is negative, so the force on Q2 will be to the right.
so the idea is to set the two forces MAGNITUDEs equal (you know the directions are opposite already).
KQ1Q2/x^2=KQ2Q3/(.5-x)^2
where you are putting all + charges (you need magnitudes). x is the distance from q1, and .5-x is the distance from Q3.
solve for x
i know how to get to that point. but how would you solve for x. i know you can use the quadratic equation. but im not sure how to
To find the net electrostatic force on Q3, we need to calculate the individual forces between each pair of charges and then add them up.
The formula to calculate the electrostatic force between two charges is given by Coulomb's Law:
F = k * (|Q1| * |Q2|) / r^2
where F is the electrostatic force, k is the Coulomb's constant (k ≈ 9.0 x 10^9 N*m^2/C^2), |Q1| and |Q2| are the absolute values of the charges, and r is the distance between the charges.
Let's calculate the forces between each pair of charges:
1. Force on Q3 due to Q1:
Absolute value of Q1: |Q1| = |-8mC| = 8mC
Distance between Q1 and Q3: r1 = 0.2 m
Force1 = k * (|Q1| * |Q3|) / r1^2
Substituting the values:
Force1 = (9.0 x 10^9 N*m^2/C^2) * (8mC * 4mC) / (0.2 m)^2
2. Force on Q3 due to Q2:
Absolute value of Q2: |Q2| = |+3mC| = 3mC
Distance between Q2 and Q3: r2 = 0.2 m
Force2 = k * (|Q2| * |Q3|) / r2^2
Substituting the values:
Force2 = (9.0 x 10^9 N*m^2/C^2) * (3mC * 4mC) / (0.2 m)^2
Now, we can find the net electrostatic force on Q3 by adding these two forces:
Net Force on Q3 = Force1 + Force2
Substituting the calculated values, we can find the net electrostatic force on Q3.