Final answer:
To find the point on the x-axis where a – 45 nC charge experiences no net force given other charges on the axis, one must consider the forces exerted by these charges. The charge must be placed closer to the weaker 3.0 nC charge than the stronger – 12 nC charge, likely at x= -4.0 cm.
Step-by-step explanation:
The student is asking where to place a – 45 nC charge on the x-axis, so it experiences no net force, considering there are already two charges located on the x-axis: a 3.0 nC charge at the origin (x=0) and a – 12 nC charge at x=2.0 cm.
To solve this, we need to find a point where the forces exerted on the – 45 nC charge by the other two charges cancel out. The force between two charges is given by Coulomb's Law:
F = k * |q1 * q2| / r²
Where F is the force, k is Coulomb's constant, q1 and q2 are the charges, and r is the distance between the charges.
The negative charge will be repelled by the – 12 nC charge and attracted to the 3.0 nC charge. Since the 3.0 nC charge is weaker than the – 12 nC charge, the – 45 nC charge must be closer to the 3.0 nC charge in order for the forces to balance. As the options given are to the left of the – 12 nC charge (where the – 45 nC charge would be repelled to) and to the right of the 3.0 nC charge (where it would be attracted to), the correct answer must be one of the options on the left side. Intuitively, we can eliminate x= -1.0 cm and x= -2.0 cm as these are too close to the – 12 nC charge, leaving us with x= -4.0 cm as the most likely location where the net force would be zero.