Final answer:
To find the point on the x-axis between two charges where the electric field is zero, we can use the principle of superposition. The point on the x-axis where the electric field is zero is x = -0.017 m.
Step-by-step explanation:
To find the point on the x-axis between two charges where the electric field is zero, we can use the principle of superposition. The electric field at a point between two charges is the vector sum of the electric fields produced by each charge individually. Therefore, to find the point where the electric field is zero, we need to find the point where the electric fields due to the two charges cancel out.
In this case, we have two charges: -3.0μC at (-0.50m, 0) and -4.0μC at (0.50m, 0). Since the charges are negative, the electric fields they produce are directed towards them. At a point on the x-axis, the electric field due to the -3.0μC charge will be directed towards the left, and the electric field due to the -4.0μC charge will be directed towards the right. Therefore, to find the point where the electric field is zero, we need to find the distance between the charges where the magnitudes of the electric fields are equal.
Using Coulomb's Law, we can calculate the electric field due to each charge at a given distance. The electric field due to a point charge is given by the equation:
E = k * (q / r^2)
where E is the electric field, k is Coulomb's constant (9.0 x 10^9 N m^2/C^2), q is the charge, and r is the distance from the charge. By setting these two equations equal to each other and solving for the distance, we can find the point on the x-axis where the electric field is zero.
Using this method, the point on the x-axis between the two charges where the electric field is zero would be at x = -0.017 m or x = 0.017 m. If the coordinate system is defined such that the positive x-axis is to the right, then the point at x = -0.017 m (to the left of the origin) is where the electric field is zero. At the origin, the electric field will not be zero.