charge +2micro coulomb is placed at a pointA(2,1,0). another charge-3 microcoulomb placed at B(4,2,-1). find the net force on charge +5micro coulomb placed at a point C(-1,3,2)
To find the net force on the charge placed at point C, we need to calculate the force exerted by each of the charges at point C and then add them together as vectors.
The force between two charges can be calculated using Coulomb's Law, which states that the magnitude of the electric 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.
Let's calculate the force between the charge at A and C first. The formula for the electric force is:
F = k * (|q1| * |q2|) / r^2
where:
- F is the magnitude of the force
- k is the Coulomb's constant (k ≈ 9 x 10^9 Nm^2/C^2)
- |q1| and |q2| are the magnitudes of the charges
- r is the distance between the charges
Calculating for the force between A and C:
- |q1| = 2 microcoulomb = 2 x 10^(-6) C
- |q2| = 5 microcoulomb = 5 x 10^(-6) C
- r = distance between A(2,1,0) and C(-1,3,2)
Using the distance formula:
r = sqrt((x2 - x1)^2 + (y2 - y1)^2 + (z2 - z1)^2)
Substituting the values:
r = sqrt((2 - (-1))^2 + (1 - 3)^2 + (0 - 2)^2)
= sqrt(3^2 + (-2)^2 + (-2)^2)
= sqrt(9 + 4 + 4)
= sqrt(17)
Now, we have all the values to calculate the force between A and C:
F1 = k * (|q1| * |q2|) / r^2
= (9 x 10^9 Nm^2/C^2) * ((2 x 10^(-6) C) * (5 x 10^(-6) C)) / (sqrt(17))^2
Solving this will give us the magnitude of the force between A and C.
Next, we need to calculate the force between B and C using the same steps as above:
- |q1| = 3 microcoulomb = 3 x 10^(-6) C
- |q2| = 5 microcoulomb = 5 x 10^(-6) C
- r = distance between B(4,2,-1) and C(-1,3,2)
Using the distance formula:
r = sqrt((x2 - x1)^2 + (y2 - y1)^2 + (z2 - z1)^2)
Substituting the values:
r = sqrt((4 - (-1))^2 + (2 - 3)^2 + (-1 - 2)^2)
= sqrt(5^2 + (-1)^2 + (-3)^2)
= sqrt(25 + 1 + 9)
= sqrt(35)
Calculating the force between B and C:
F2 = k * (|q1| * |q2|) / r^2
= (9 x 10^9 Nm^2/C^2) * ((3 x 10^(-6) C) * (5 x 10^(-6) C)) / (sqrt(35))^2
Solving this will give us the magnitude of the force between B and C.
Finally, to find the net force on the charge placed at point C, we simply add the forces F1 and F2 together as vectors. The net force will have both magnitude and direction, which can be determined using vector addition.
F_net = F1 + F2
Remember to include the direction of the forces when adding them together.