To solve this problem, we first need to find the point on the x-axis where the electric field due to these two charges is zero. The electric field E due to a point charge q at a distance r is given by E = kq/r^2, where k is Coulomb's constant (8.99 x 10^9 N m^2/C^2).

The electric field due to the two charges will be zero at a point where the magnitudes of the individual electric fields due to the two charges are equal. This will occur at two points - one between the charges and one outside.

1. For the point between the charges:

Let's denote the distance from the -6.10 nC charge to the point where the electric field is zero as x. Then the distance from the 21.4 nC charge to this point is 11.4 cm - x. Setting the magnitudes of the electric fields due to the two charges equal gives:

|E1| = |E2|
k|-6.10 nC|/x^2 = k|21.4 nC|/(11.4 cm - x)^2

Solving this equation for x gives the location of the point between the charges where the electric field is zero.

2. For the point outside the charges:

If the point where the electric field is zero is to the right of the 21.4 nC charge, then the distance from the -6.10 nC charge to this point is x + 11.4 cm, and the distance from the 21.4 nC charge to this point is x. Setting the magnitudes of the electric fields due to the two charges equal gives:

|E1| = |E2|
k|-6.10 nC|/(x + 11.4 cm)^2 = k|21.4 nC|/x^2

Solving this equation for x gives the location of the point outside the charges where the electric field is zero.

3. Calculate the electric potential:

Once we have the locations of the points where the electric field is zero, we can calculate the electric potential V at these points. The electric potential due to a point charge q at a distance r is given by V = kq/r. The total electric potential at a point due to multiple charges is the sum of the electric potentials due to the individual charges.

For the point between the charges, the electric potential is V = k(-6.10 nC)/x + k(21.4 nC)/(11.4 cm - x).

For the point outside the charges, the electric potential is V = k(-6.10 nC)/(x + 11.4 cm) + k(21.4 nC)/x.

These are the electric potentials at the points on the x-axis where the electric field due to the two charges is zero.

Question

To solve this problem, we first need to find the point on the x-axis where the electric field due to these two charges is zero. The electric field E due to a point charge q at a distance r is given by E = kq/r^2, where k is Coulomb's constant (8.99 x 10^9 N m^2/C^2).

The electric field due to the two charges will be zero at a point where the magnitudes of the individual electric fields due to the two charges are equal. This will occur at two points - one between the charges and one outside.

1. For the point between the charges:

Let's denote the distance from the -6.10 nC charge to the point where the electric field is zero as x. Then the distance from the 21.4 nC charge to this point is 11.4 cm - x. Setting the magnitudes of the electric fields due to the two charges equal gives:

|E1| = |E2|
k|-6.10 nC|/x^2 = k|21.4 nC|/(11.4 cm - x)^2

Solving this equation for x gives the location of the point between the charges where the electric field is zero.

2. For the point outside the charges:

If the point where the electric field is zero is to the right of the 21.4 nC charge, then the distance from the -6.10 nC charge to this point is x + 11.4 cm, and the distance from the 21.4 nC charge to this point is x. Setting the magnitudes of the electric fields due to the two charges equal gives:

|E1| = |E2|
k|-6.10 nC|/(x + 11.4 cm)^2 = k|21.4 nC|/x^2

Solving this equation for x gives the location of the point outside the charges where the electric field is zero.

3. Calculate the electric potential:

Once we have the locations of the points where the electric field is zero, we can calculate the electric potential V at these points. The electric potential due to a point charge q at a distance r is given by V = kq/r. The total electric potential at a point due to multiple charges is the sum of the electric potentials due to the individual charges.

For the point between the charges, the electric potential is V = k(-6.10 nC)/x + k(21.4 nC)/(11.4 cm - x).

For the point outside the charges, the electric potential is V = k(-6.10 nC)/(x + 11.4 cm) + k(21.4 nC)/x.

These are the electric potentials at the points on the x-axis where the electric field due to the two charges is zero.

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