Three charged objects are located t the vertices of a right triangle. Charge A (5*10^-6) has Cartesian coordinates (0,4; Charge B (-5.0*10^-6) is at the origin; charge c (+4.0*10^-6) has coordinates (5,0), where the coordinates are in meters. What is the net force on each charge.
Ans: I found the charge on B by finding the force F(a to b) and similarly the hypotenuse force and using the cosine rule and sine rule i found the direction and the net charge but when i try the same on point charges A and C i do not get the answer. Where am i going wrong?
The desired answers according to the textbook seem to be Fa=1.2 x 10^-2 N [W73 S]; Fa=1.6 x 10^-2 N [W63 S]; Fa=4.6 x 10^-3 N [W31 S];
Thing is, using those formulas I don't get the correct answers at all. From the triangle, we have a side with 4m, a side with 5m, and (Found using the Pythagorean theorem) a side with 6.4m. When using the formulas given I get Fa= 1.4x10^-2 N and the 73 degrees; then for the B i get the correct answers. For Fc I get 8.4x10^-3 and a 31 degree angle.... help
Pick a charge: Say B. Find Fab and Fac. Note: Fba=-Fab and Fca=-Fac
so you have now only one other force, Fbc. Fcb=-Fbc
So you have had to calculate only three pairs of charges.
The for magnitude, consider NOT using the trig resolutions, do this
Fa^2= Fab^2+Fac^2
Fb^2=Fba^2+Fbc^2
Fc^2=Fca^2+Fcb^2
That is it.
To find the net force on charges A and C, you can use Coulomb's law, which gives the force between two point charges. Coulomb's law states that the magnitude of the force between two charges is given by:
F = k * (|q1| * |q2|) / r^2
where F is the magnitude of the force, k is the electrostatic constant (approximately 9 × 10^9 N m^2/C^2), q1 and q2 are the charges, and r is the distance between the charges.
For charge A (5 * 10^-6 C):
- Calculate the distance between charge A and charge B (at the origin), which is the length of the hypotenuse of the right triangle. Using the distance formula:
d(A to B) = √(x2 - x1)^2 + (y2 - y1)^2 = √(0 - 0)^2 + (4 - 0)^2 = 4 m
- Calculate the distance between charge A and charge C:
d(A to C) = √(x2 - x1)^2 + (y2 - y1)^2 = √(5 - 0)^2 + (0 - 4)^2 = √(25 + 16) = √41 m
Now, calculate the magnitude of the force between charge A and charge B:
F(A to B) = (k * |q1| * |q2|) / r^2 = (9 × 10^9 N m^2/C^2) * |5 × 10^-6 C| * |-5 × 10^-6 C| / (4 m)^2
= 45 × 10^-9 N
Calculate the magnitude of the force between charge A and charge C:
F(A to C) = (k * |q1| * |q2|) / r^2 = (9 × 10^9 N m^2/C^2) * |5 × 10^-6 C| * |4 × 10^-6 C| / (√41 m)^2
= 180 × 10^-9 N
The net force on charge A is the vector sum of F(A to B) and F(A to C). To find the direction of this net force, you can use trigonometry. By decomposing the forces along the x-axis and y-axis, you can find the x-component and y-component of the net force separately.
For charge C (4 * 10^-6 C):
- Calculate the distance between charge C and charge B (at the origin), which is the length of the hypotenuse of the right triangle. Using the distance formula:
d(C to B) = √(x2 - x1)^2 + (y2 - y1)^2 = √(0 - 5)^2 + (0 - 4)^2 = √(25 + 16) = √41 m
- Calculate the distance between charge C and charge A:
d(C to A) = √(x2 - x1)^2 + (y2 - y1)^2 = √(5 - 0)^2 + (0 - 4)^2 = 4 m
Now, calculate the magnitude of the force between charge C and charge B:
F(C to B) = (k * |q1| * |q2|) / r^2 = (9 × 10^9 N m^2/C^2) * |4 × 10^-6 C| * |-5 × 10^-6 C| / (√41 m)^2
= 180 × 10^-9 N
Calculate the magnitude of the force between charge C and charge A:
F(C to A) = (k * |q1| * |q2|) / r^2 = (9 × 10^9 N m^2/C^2) * |4 × 10^-6 C| * |5 × 10^-6 C| / (4 m)^2
= 45 × 10^-9 N
The net force on charge C is the vector sum of F(C to B) and F(C to A). To find the direction of this net force, you can use trigonometry. By decomposing the forces along the x-axis and y-axis, you can find the x-component and y-component of the net force separately.
When dealing with point charges, the net force on each charge can be calculated using Coulomb's Law. Coulomb's Law states that the magnitude of the electrostatic force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
To calculate the force between charge A and charge B (FAB), you correctly used Coulomb's Law. The distance between charge A and B is the hypotenuse of the right triangle, which can be calculated using the Pythagorean theorem.
To calculate the force between charge A and charge C (FAC), and charge B and charge C (FBC), you need to calculate the distances between these charges using the distance formula:
Distance between A and C: sqrt((x2 - x1)^2 + (y2 - y1)^2)
Distance between B and C: sqrt((x2 - x1)^2 + (y2 - y1)^2)
Once you have the distances, you can use Coulomb's Law to calculate the forces, keeping in mind that the direction of the forces will depend on the coordinates of the charges.
To find the net force on each charge, you need to consider both the magnitude and direction of the forces acting on each charge. The net force on a charge is the vector sum of the individual forces acting on it. To calculate the net force, you can use vector addition.
Net force on charge A: The net force on charge A is the vector sum of FAB and FAC.
Net force on charge B: The net force on charge B is the vector sum of FAB and FBC.
Net force on charge C: The net force on charge C is the vector sum of FAC and FBC.
By calculating the magnitudes and directions (angles) of the forces using Coulomb's Law, and then using vector addition to find the net forces, you should be able to obtain the correct answer for the net force on each charge.