Final answer:
The electric field at point P is zero when the electric fields due to charges q1 and q2 cancel each other. The distance x from q1 to P where this happens can be found by equating the magnitudes of the electric fields from both charges and solving for x.
Step-by-step explanation:
The question is asking for the distance from charge q1 to a point P where the electric field is zero. To find this distance, we use the principle that at point P, the electric fields due to both charges must cancel each other out. This is because the electric field due to a point charge is given by E = k*q/r^2, where E is the electric field, k is Coulomb's constant (8.988 × 10^9 Nm^2/C^2), q is the charge, and r is the distance from the charge.
Let x be the distance from q1 (-32 mc) to point P and (12 cm - x) be the distance from point P to q2 (45 mc). Seeing that q2 is positive and q1 is negative, point P must be closer to q1 for the fields to cancel. Setting up the equation based on their electric fields, we have k*|q1|/x^2 = k*q2/(12-x)^2. We can solve this equation for x to find the distance where the electric field is zero. The microcoulomb (mc) should be converted to coulomb (C) by multiplying by 10^-6 for proper calculations.