Three point charges are located on the x-axis. The first charge, q1 = 10.0 µC, is at x = -1.00 m; the second charge, q2 = 20.0 µC, is at the origin; and the third charge, q3 = -30.0 µC, is located at x = 2.00 m. Which charge is subjected to the force of greatest magnitude?
q1
q2
q3
q1 and q2 (equal)
q2 and q3 (equal)
u didnt convert uC to C ^^^^^^^^^^
To determine which charge is subjected to the force of the greatest magnitude, we need to calculate the electric force between each pair of charges using Coulomb's Law and compare their magnitudes.
The electric force between two charges is given by Coulomb's Law:
F = k * |q1 * q2| / r^2
Where:
- F is the magnitude of the force
- k is the electrostatic constant (k = 9.0 × 10^9 N·m^2/C^2)
- q1 and q2 are the charges
- r is the distance between the charges
Let's calculate the forces between the charges:
1) Force between q1 and q2:
Distance between q1 and q2 (r12) = 1.00 m (distance from -1.00 m to the origin)
F12 = k * |q1 * q2| / r12^2
= (9.0 × 10^9 N·m^2/C^2) * |(10.0 µC) * (20.0 µC)| / (1.00 m)^2
2) Force between q2 and q3:
Distance between q2 and q3 (r23) = 2.00 m (distance from the origin to 2.00 m)
F23 = k * |q2 * q3| / r23^2
= (9.0 × 10^9 N·m^2/C^2) * |(20.0 µC) * (-30.0 µC)| / (2.00 m)^2
Now, let's calculate the magnitudes of these forces and determine which one is greatest.
To determine which charge is subjected to the force of greatest magnitude, we need to calculate the force between each pair of charges using Coulomb's Law:
F = k * |q1 * q2| / r^2
Where:
- F is the magnitude of the force between the charges
- k is the electrostatic constant (k = 8.99 x 10^9 N m^2/C^2)
- |q1 * q2| is the product of the magnitudes of the charges
- r is the distance between the charges.
Let's calculate the forces acting on each charge:
1. Force between q1 and q2:
Charge q1 = 10.0 µC = 10.0 x 10^-6 C
Charge q2 = 20.0 µC = 20.0 x 10^-6 C
Distance between q1 and q2 = 1.00 m
Using Coulomb's Law: F12 = k * |q1 * q2| / r^2 = (8.99 x 10^9 N m^2/C^2) * |10.0 x 10^-6 C * 20.0 x 10^-6 C| / (1.00 m)^2
2. Force between q2 and q3:
Charge q2 = 20.0 µC = 20.0 x 10^-6 C
Charge q3 = -30.0 µC = -30.0 x 10^-6 C
Distance between q2 and q3 = 2.00 m
Using Coulomb's Law: F23 = k * |q2 * q3| / r^2 = (8.99 x 10^9 N m^2/C^2) * |20.0 x 10^-6 C * -30.0 x 10^-6 C| / (2.00 m)^2
Now let's compare the magnitudes of these forces to determine which one is greatest.
net force on q1: kq1q2/1^2+kq1q2/3^2= k(10*20)/1+k(10(-30))/9
= k 200-33 to left Ignoring units
net chage on q2: kq2q1/1^2 +kq2q3/2^2= 200k (to left) +600k/4 to right
= k150 to left
net force on q3= kq3q1/9 (to left) + kq3q2/4
= k30/9 to left + k600/9 (to left) + k30*20/4 to left
= k217 to left
check my math and direction of forces