To find the x-coordinate of the point where the net force on a point charge of 0.300 μC is zero, we need to calculate the net force at different x-coordinates and find where it equals zero.
The net force between two charges can be calculated using Coulomb's Law:
F = k * (|q1| * |q2|) / r^2
Where:
F is the net force
k is the electrostatic constant (k = 8.99 x 10^9 Nm^2/C^2)
|q1| and |q2| are the magnitudes of the charges
r is the distance between the charges
Let's calculate the net force at different x-coordinates:
For x = -4.7 m:
F1 = k * (|q1| * |q3|) / r1^2
= (8.99 x 10^9 Nm^2/C^2) * (|3.94 µC| * |0.300 μC|) / (-4.7 m)^2
For x = 12.2 m:
F2 = k * (|q2| * |q3|) / r2^2
= (8.99 x 10^9 Nm^2/C^2) * (|6.14 µC| * |0.300 μC|) / (12.2 m)^2
We want to find the x-coordinate where the net force is zero, so we can set F1 + F2 = 0.
F1 + F2 = 0
k * (|q1| * |q3|) / r1^2 + k * (|q2| * |q3|) / r2^2 = 0
Let's solve this equation to find the x-coordinate.
As shown in the figure, charge 1 is 3.94 µC and is located at x₁ = -4.7 m, and charge 2 is 6.14 µC and is at x2 = 12.2 m. What is the x-coordinate of the point at which the net force on a point charge of 0.300 μC is zero?
1 answer