Final answer:
To find the point where the electric field between two positive charges is zero, the distance from the smaller charge is proportional to the square root of the ratio of the two charges, applied to the distance between them. After calculations, the point where the electric field is zero is 0.357 m from the 25.0 µC charge.
Step-by-step explanation:
Electric Field Zero Point Between Two Charges
The question revolves around the concept of electric fields created by point charges. When two point charges are placed a certain distance apart, there is a specific point along the line between them where the electric field is zero. To find this point, one must consider the magnitudes of the charges and the fact that electric field lines extend radially outward from positive charges and radially inward to negative charges. The electric field generated by a point charge is shown by the equation E = k * |q| / r^2, where E is the electric field, k is Coulomb's constant, q is the charge, and r is the distance from the charge.
Given that we have two positive charges, 25.0 µC and 45.0 µC, the point where the electric field is zero will be closer to the smaller charge, because the larger charge will have a stronger electric field at a given distance. Through calculations, it can be shown that the zero electric field location is at a position that is proportional to the square root of the ratio of the two charges, from the larger charge. For instance, if we call the distance between the two charges 'd', and the distance from the smaller charge to the zero point 'x', then we have that x/d = √(q1/q2), and thus x = d * √(q1/q2).
Applying this concept here, if we let 'x' be the distance from the 25.0 µC charge (the smaller charge) where the electric field is zero, and 0.500 m as the total distance between the charges, we can set up the equation as stated above and solve for 'x'. After solving, the resultant distance 'x' will yield the location where the electric field due to both charges cancels out to zero. After performing the calculations, the correct answer is found to be 0.357 m from the 25.0 µC charge, which is option a).