Three charges are located along the x axis as shown in the drawing. The mass of the -1.2 uC is 4.0×10^-9 kg. Determine the magnitude and direction of the acceleration of the -1.2 uC charge when it is allowed to move if the other two charges remain fixed. I need help remembering what formulas and equations come into play here
To determine the magnitude and direction of the acceleration of a charged particle, we need to use Newton's second law of motion and the electric force equation.
1. Newton's Second Law of Motion: This law states that the force acting on an object is equal to the mass of the object multiplied by its acceleration. Mathematically, it can be written as F = m*a, where F is the force, m is the mass, and a is the acceleration.
2. Electric Force Equation: The electric force between two charged objects is given by Coulomb's law, which states that the magnitude of the force is directly proportional to the product of the two charges and inversely proportional to the square of the distance between them. Mathematically, it can be written as F = k*(q1*q2)/r^2, where F is the force, k is the electrostatic constant (9 × 10^9 N m^2/C^2), q1 and q2 are the charges, and r is the distance between the charges.
Using these two equations, we can calculate the acceleration of the -1.2 uC charge. Let's assume the charges are labeled as follows:
q1 = +3.6 uC (positive charge) at the origin (0, 0)
q2 = -2.4 uC (negative charge) at x = 0.04 m
q3 = -1.2 uC (negative charge) at x = 0.08 m
The total force acting on q3 will be the sum of the forces due to q1 and q2. Since q1 and q2 are fixed, the distance between q3 and each of the other charges remains constant.
To find the acceleration, we can use Newton's second law:
F_net = m*a
To find the net force, we need to find the forces exerted by q1 and q2 on q3:
F_net = F1 + F2
Where F1 is the force exerted by q1 on q3, and F2 is the force exerted by q2 on q3.
Using Coulomb's law, we can calculate the force between q1 and q3:
F1 = k*(q1*q3)/r1^2
Similarly, we can calculate the force between q2 and q3:
F2 = k*(q2*q3)/r2^2
Finally, we substitute these forces into the net force equation and divide by the mass of q3 to find the acceleration:
a = (F1 + F2)/m
By plugging in the given values and performing the calculations, you will be able to find the magnitude and direction of the acceleration of the -1.2 uC charge.