Electrostatic Two negative point charges q1 and q2 are separated in a vacuum by a distance of 3.0 m. Charge q1 is four times as great as charge q2. If the net electric force is zero at the spot on the line between the charges and at a distance of 1.0 m from q2 , find the value of the charges q1 and q2?

Question

Answer

Given information:
- Two negative point charges q1 and q2 are separated in a vacuum by a distance of 3.0 m.
- Charge q1 is four times as great as charge q2.
- The net electric force is zero at the spot on the line between the charges and at a distance of 1.0 m from q2.

Calculating the charges q1 and q2:

Let's assume that q2 is the smaller charge and q1 is four times as great as q2. So, we can write:

q1 = 4q2

Calculating the distance from q1 to the point where the net electric force is zero:

The distance from q1 to the point where the net electric force is zero is 3.0 m - 1.0 m = 2.0 m.

Applying Coulomb's Law:

According to Coulomb's Law, the electric force between two charges is given by the equation:

F = k * |q1| * |q2| / r^2

Where F is the electric force, k is the electrostatic constant (k = 8.99 x 10^9 N m^2/C^2), q1 and q2 are the charges, and r is the distance between the charges.

Calculating the electric force between q1 and the point:

Since the net electric force is zero at the point, the electric force between q1 and the point should be equal in magnitude but opposite in direction to the electric force between q2 and the point.

So, we can write:

F1 = -F2

Substituting the values into the equation:

k * |q1| * |q2| / (2.0 m)^2 = -k * |q1| * |q2| / (1.0 m)^2

Simplifying the equation:

We can cancel out the electrostatic constant and the absolute values of q1 and q2:

4 * q2 / (2.0 m)^2 = -q2 / (1.0 m)^2

Simplifying further:

4 * q2 = -q2 * 4

Calculating the charges:

From the equation above, we can see that q2 = -q2, which implies q2 = 0.

Substituting q2 = 0 into the equation q1 = 4q2:

q1 = 4 * 0 = 0

Therefore, the value of q1 is 0 and the value of q2 is also 0.

Conclusion:

The charges q1 and q2 are both 0.

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