Two charges are arranged on the x axis so that there is a positive charge of 3.6 micro C at the orgin and a negative charge of -2.5 micro C located 2 centimeters to its right. to the nearest centimeter, where on the x axis should a positive charge be placed so that the net force on it is zero?
To find the position on the x-axis where a positive charge should be placed so that the net force on it is zero, we need to ensure that the electrostatic forces exerted by the two charges cancel each other out.
The electrostatic force between two charges is given by Coulomb's Law:
F = k * |q1 * q2| / r^2
Where F is the force, k is the electrostatic constant (9 x 10^9 N*m^2/C^2), q1 and q2 are the magnitudes of the charges, and r is the distance between the charges.
Let's calculate the net electrostatic force acting on the positive charge due to the other two charges:
Force due to the positive charge at the origin (q1 = 3.6 µC):
F1 = k * |q1 * q3| / r1^2
Force due to the negative charge located 2 centimeters to the right (q2 = -2.5 µC):
F2 = k * |q2 * q3| / r2^2
Since we want the net force to be zero, the magnitudes of these forces should be equal:
|F1| = |F2|
Let's calculate the distances and solve for the position of the positive charge (q3):
Distance from the origin to the positive charge (r1) = x cm
Distance from the positive charge to the negative charge (r2) = 2 cm
Now we can set up the equation:
k * |q1 * q3| / r1^2 = k * |q2 * q3| / r2^2
Substituting the given values:
(9 x 10^9 N*m^2/C^2) * (3.6 x 10^-6 C * q3) / (x cm)^2 = (9 x 10^9 N*m^2/C^2) * (-2.5 x 10^-6 C * q3) / (2 cm)^2
Simplifying further:
(3.6 * q3) / x^2 = (-2.5 * q3) / 4
Now, we can solve for x:
(3.6 * q3) / x^2 = (-2.5 * q3) / 4
Cross-multiplying and simplifying:
(3.6 * q3) * 4 = (-2.5 * q3) * x^2
14.4 * q3 = -2.5 * q3 * x^2
Dividing both sides by q3:
14.4 = -2.5 * x^2
Now we can solve for x^2:
x^2 = 14.4 / (-2.5)
x^2 = -5.76
Since we cannot have a negative distance, this means that there is no position on the x-axis where the net force on the positive charge is zero.