A charge q1=7.8x10^-6 C is placed at the origin. q2=-3.4x10^-6 C is placed at y=-1 m, x=2 m. q3=-9.2x10^-6 C is placed at y=4 m. What is the total force on q1? On q3?
To find the total force on a charged object, we can use Coulomb's Law, which states that the force between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
The formula for Coulomb's Law is:
F = (k * |q1 * q2|) / r^2
Where:
F is the force between the charged objects
k is the Coulomb's constant (k = 9 x 10^9 N m^2/C^2)
q1 and q2 are the charges of the objects
r is the distance between the objects
First, let's calculate the force on q1:
q1 = 7.8 x 10^-6 C
q2 = -3.4 x 10^-6 C
The distance between q1 and q2 can be calculated using the Pythagorean theorem:
d1 = √(x^2 + y^2) (distance between q1 and q2)
Given:
x = 2 m (horizontal distance)
y = -1 m (vertical distance)
d1 = √(2^2 + (-1)^2) = √(4 + 1) = √5
Now, we can calculate the force between q1 and q2:
F1 = (k * |q1 * q2|) / r^2
= (9 x 10^9 N m^2/C^2) * |(7.8 x 10^-6 C) * (-3.4 x 10^-6 C)| / (√5)^2
= 9 x 10^9 * (7.8 x 10^-6) * (3.4 x 10^-6) / 5
Now, let's calculate the force on q3:
q3 = -9.2 x 10^-6 C
The distance between q1 and q3 can also be calculated using the Pythagorean theorem:
d2 = √(x^2 + y^2) (distance between q1 and q3)
Given:
x = 0 m (horizontal distance)
y = 4 m (vertical distance)
d2 = √(0^2 + 4^2) = 4
Now, we can calculate the force between q1 and q3:
F2 = (k * |q1 * q3|) / r^2
= (9 x 10^9 N m^2/C^2) * |(7.8 x 10^-6 C) * (-9.2 x 10^-6 C)| / 4^2
= 9 x 10^9 * (7.8 x 10^-6) * (9.2 x 10^-6) / 16
Therefore, you can calculate the force on q1 and q3 using the given charges and distances.