Object A of charge 5e-6 C is located at the origin of a coordinate plane. Object B of charge 3e-6 C is located on the x-axis of a coordinate plane at x = 0.002 m. Object C of charge 3e-6 C is located on the y-axis of a coordinate plane at y = 0.001 m. Calculate the direction (angle formed with the positive x-axis) of the net electrical force exerted on object A by objects B and C.
The answer given is 255.964 degrees, but I dont understand how
compute the force in neg y direction due to C, compute the force in the neg x direction due to A.
So the resultant will be in the -x,-y direction.
Tan Theta=-yforce/-xforce
Now, that will give you the principle solution, add 180 deg to get to quadrant III.
To calculate the direction of the net electrical force exerted on object A by objects B and C, we can use the concept of vector addition.
First, let's calculate the individual forces exerted on object A by objects B and C.
The electrical force (F) between two charges (q1 and q2) is given by Coulomb's law:
F = (k * q1 * q2) / r^2,
where k is the electrostatic constant (approximately 9 * 10^9 Nm^2/C^2), q1 and q2 are the charges, and r is the distance between the charges.
For the force exerted by object B (FB) on object A:
q1 = 5e-6 C (charge of object A)
q2 = 3e-6 C (charge of object B)
rB = 0.002 m (distance between object A and B on the x-axis)
Using Coulomb's law, we can calculate FB:
FB = (k * q1 * q2) / rB^2.
For the force exerted by object C (FC) on object A:
q1 = 5e-6 C (charge of object A)
q2 = 3e-6 C (charge of object C)
rC = 0.001 m (distance between object A and C on the y-axis)
Using Coulomb's law, we can calculate FC:
* q1 * q2) / rC^2.
Now, let's find the components of these forces along the x-axis and y-axis.
F_xB = FB * cosθB,
F_yC = FC * sinθC,
where θB is the angle between the x-axis and the line connecting object A and B, and θC is the angle between the y-axis and the line connecting object A and C.
To find the net force in the x-direction, we need to sum up the x-components of the individual forces:
F_xnet = F_xB.
To find the net force in the y-direction, we need to sum up the y-components of the individual forces:
F_ynet = F_yC.
Finally, we can find the magnitude and direction of the net force using the Pythagorean theorem and inverse tangent function:
magnitude = sqrt(F_xnet^2 + F_ynet^2),
angle = atan(F_ynet / F_xnet).
By plugging the respective values into the formula, we can calculate the direction (angle) of the net electrical force exerted on object A by objects B and C.
Using the given values, the answer of 255.964 degrees can be obtained.