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We are tasked with finding the distance \( r_1 \) from a point charge where the electric potential is 120 V, given the charge is \( 1.9 \, \mu C \). 

The formula for the electric potential \( V \) due to a point charge \( Q \) is given by:

\[
V = \frac{kQ}{r}
\]

Where:
- \( V \) is the electric potential,
- \( k \) is Coulomb's constant, approximately \( 8.99 \times 10^9 \, \text{Nm}^2/\text{C}^2 \),
- \( Q \) is the charge in coulombs, and
- \( r \) is the distance from the charge.

We can rearrange this equation to solve for \( r \):

\[
r = \frac{kQ}{V}
\]

Given:
- \( Q = 1.9 \, \mu C = 1.9 \times 10^{-6} \, \text{C} \),
- \( V = 120 \, \text{V} \),
- \( k = 8.99 \times 10^9 \, \text{Nm}^2/\text{C}^2 \),

we can now compute \( r_1 \). Let me calculate that for you.The distance \( r_1 \) from the charge where the potential is 120 V is approximately \( 142.34 \, \text{meters} \).

Would you like further details or have any questions?

Here are 5 related questions for deeper understanding:
1. How would the potential change if the charge were doubled?
2. What happens to the potential as the distance approaches infinity?
3. How would you calculate the potential at a distance of 50 meters from this charge?
4. What is the electric field at the distance \( r_1 \)?
5. How would the result change if the medium between the charge and point of measurement was not vacuum?

**Tip:** Always ensure that the charge is in Coulombs (C) and distances in meters (m) when using Coulomb's law to avoid unit errors.

Suppose you have a 1.9 µC point charge. How far in meters from the charge will the potential be 120 V if it is zero at infinity?

Discover how to calculate the distance from a point charge where the electric potential is 120 V, given a charge of 1.9 µC. This problem employs Coulomb's law for electric potential, ideal for university-level physics students.

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