If the potential due to a point charge is 709 V at a distance of 11.8 m, what is the magnitude of the charge?

Use a value of 9.00x109 N.m2/C2 for Coulomb's constant, k.

Write your answer in the units of micro-coulomb (
𝜇
𝐶
) to the third decimal place, e.g. 1.263

Do not include units in your answer; just write the numerical value.

Question

If the potential due to a point charge is 709 V at a distance of 11.8 m, what is the magnitude of the charge?

Use a value of 9.00x109 N.m2/C2 for Coulomb's constant, k.

Write your answer in the units of micro-coulomb (
𝜇
𝐶
) to the third decimal place, e.g. 1.263

Do not include units in your answer; just write the numerical value.

BlackTom AI · Accepted Answer

Let's parse the key givens and apply the relation between electric potential and a point charge.
The potential at distance r from a point charge q is V = k q / r, where k is Coulomb's constant.
We are given V = 709 V, r = 11.8 m, and k = 9.00×10^9 N·m^2/C^2. The goal is to find q and then express it in microcoulombs.
Rearranging the formula gives q = V r / k.
Compute the numerator first: V × r = 709 × 11.8.
Breakdown: 700 × 11.8 = 8260, and 9 × 11.8 = 106.2; add them to get 8366.2.
Now divide by k: q = 8366.2 / (9.00×10^9).
Perform the division: 8366.2 ÷ 9.00×10^9 ≈ 9.295×10^−7 C.
To express in microcoulombs, recall 1 μC = 1×10^−6 C, so q ≈ 0.9295 μC.
Rounding to three decimal places yields 0.930 μC.
Since the prompt asks for the numerical value without units, the final numeric value is 0.930, consistent with the calculation above.
Answer check: if you substitute q ≈ 9.30×10^−7 C back into V = kq/r, you recover V ≈ 709 V given the provided r and k, verifying consistency.

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