Final answer:
The net electric field created by two positive point charges on the x-axis cannot be zero at any point between them on the x-axis. Therefore, none of the given options A) x = 6.0 cm, B) x = 8.0 cm, C) x = 10.0 cm, D) x = 12.0 cm can be correct.
Step-by-step explanation:
The student has asked about the position on the x-axis where the net electric field created by two point charges equals zero. The charges in question are q1=3.00 µC located at the origin and q2=6.00 µC located at x=12.0 cm on the x-axis. To find the position where the net electric field is zero, we need to set up the equation where the magnitudes of electric fields due to each charge are equal because they will have opposite directions at that point.
The electric field created by a point charge at a distance 'r' from the charge is given by E = k * |q|/r^2, where 'k' is Coulomb's constant (approximately 8.99 x 10^9 Nm^2/C^2). Let 'x' be the distance from q1 where the electric field is zero, then the distance from q2 will be (12 cm - x). Because q2 is twice as large as q1 but has the same sign, the-only position where the fields due to q1 and q2 can cancel each other is to the left of q1, that is, at a negative 'x' value. Hence, none of the given options (A to D) can be correct since they all are positive and fall between the charges.