3 charges are arranged along the x-axis.
q1 = -4.50 nC is located at x = 0.200m
q2 = +2.50 nC is located at x = -0.300m
q3 = is a positive character located at the origin.
What is the value of q3 for the net eletric force on it to be 4*10^-6 N?
I found the charge on q3 to be = 3 nC
Where along the x-axis can q3 be placed so that the net eletric force on it is 0, other than +/- infinity?
To find the value of q3 that results in a net electric force of 4*10^-6 N, we can use Coulomb's Law, which states that the electric force between two charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
Let's denote q3 as q, and let's calculate the net electric force on it due to the other charges q1 and q2.
The electric force between q1 and q3 is given by:
F1 = k * |q1| * |q| / r1^2
where k is the electrostatic constant (k ≈ 8.99 x 10^9 Nm^2/C^2), |q1| is the magnitude of q1, |q| is the magnitude of q3, and r1 is the displacement between q3 and q1 along the x-axis.
Similarly, the electric force between q2 and q3 is given by:
F2 = k * |q2| * |q| / r2^2
where |q2| is the magnitude of q2, and r2 is the displacement between q3 and q2 along the x-axis.
To find the net electric force on q3, we need to calculate the vector sum of F1 and F2:
F_net = F1 + F2
Given that the net electric force is 4*10^-6 N, we can set up the equation:
4*10^-6 N = k * |q1| * |q| / r1^2 + k * |q2| * |q| / r2^2
We know the values of |q1|, |q2|, k, r1, and r2 from the given information:
|q1| = 4.50 nC = 4.50 x 10^-9 C
|q2| = 2.50 nC = 2.50 x 10^-9 C
r1 = 0.200 m
r2 = 0.300 m
Substituting these values into the equation, we can solve for |q|:
4*10^-6 N = (8.99 x 10^9 Nm^2/C^2) * (4.50 x 10^-9 C) * |q| / (0.200 m)^2
+ (8.99 x 10^9 Nm^2/C^2) * (2.50 x 10^-9 C) * |q| / (0.300 m)^2
Simplifying the equation, we get:
4*10^-6 = (8.99 x 10^9) * (4.50 x 10^-9) * |q| / 0.04 + (8.99 x 10^9) * (2.50 x 10^-9) * |q| / 0.09
To find the value of |q| that satisfies this equation, we can rearrange and solve for |q|. However, this involves a complex equation that requires careful algebraic manipulation.
Once |q| is determined, we can find the position on the x-axis where q3 can be placed so that the net electric force on it is zero. In this case, we can set up a similar equation by setting the net electric force equal to zero and solving for the position.