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If one of the charges is removed from the pentagon, the magnitude of the electric field at the center of the pentagon becomes 9.0 N/C. How far are the vertices of the pentagon from the center of the pentagon?

Answer :

Final answer:

To find the distance of the vertices of the pentagon from the center, you need to equate the expressions for the electric fields when all charges are present and when one charge is removed and solve for the distance.

Explanation:

To calculate the distance of the vertices of the pentagon from the center, we need to first find the electric field at the center of the pentagon when all charges are present. Let's assume the charge at each vertex is Q. Then, the electric field at the center is given by E = k * Q / r², where k is the Coulomb's constant and r is the distance from the center to each vertex.

Now, if one of the charges is removed, the total charge of the pentagon becomes (4Q - Q) = 3Q. The electric field at the center can be expressed as E' = k * (3Q) / r².

Since E' = 9.0 N/C, we can equate the two expressions for E and E' and solve for r. This will give us the distance of the vertices from the center of the pentagon.

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