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A -3.0 nC charge is on the x-axis at x = -8.0 cm and a +4.0 nC charge is on the x-axis at x = 16 cm . At what point or points on the y-axis is the electric potential zero? Enter your answers numerically separated by commas. Express your answer using two significant figures.

User Danko
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Final answer:

The electric potential at a point is zero when the sum of the electric potentials due to the two charges is zero. However, in this case, there is no point on the y-axis where the electric potential is exactly zero.

Step-by-step explanation:

To find the points on the y-axis where the electric potential is zero, we can use the concept of electric potential due to a point charge. The electric potential, V, at a point due to a point charge, q, is given by the equation: V = k*q/r, where k is Coulomb's constant (9 x 10^9 Nm^2/C^2) and r is the distance between the point charge and the point of interest.

For the given charges, the electric potential at a point on the y-axis will be zero if the sum of the electric potentials due to the -3.0 nC charge and the +4.0 nC charge is zero. This means that the magnitudes of the electric potentials will be equal and opposite.

Let's calculate the electric potential at a few points on the y-axis and see if it is zero:

  1. For a point at y = 1 cm: V1 = k*(-3.0 nC)/(9.0 cm) and V2 = k*(4.0 nC)/(17.0 cm)
  2. For a point at y = 2 cm: V1 = k*(-3.0 nC)/(10.0 cm) and V2 = k*(4.0 nC)/(18.0 cm)
  3. For a point at y = 3 cm: V1 = k*(-3.0 nC)/(11.0 cm) and V2 = k*(4.0 nC)/(19.0 cm)

Based on these calculations, it seems that there is no point on the y-axis at which the electric potential is exactly zero. The closest approximation would be between the points y = 1 cm and y = 2 cm, where the difference between the two electric potentials is smallest.

User Alfakini
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