Find a point INSIDE the triangle where the electric POTENTIAL is zero when 3 point charges occupy the 3 corners of an equilateral triangle as illustrated? Please explain.
Find a point INSIDE the triangle where the electric POTENTIAL is zero when 3 point charges occupy the 3 corners of an equilateral triangle as illustrated? Please explain.
Related questions
Question
100%
![**Problem:**
Find a point INSIDE the triangle where the electric POTENTIAL is zero when 3 point charges occupy the 3 corners of an equilateral triangle as illustrated? Please explain.
**Diagram Explanation:**
- The triangle is equilateral, meaning all sides have equal length.
- There are three point charges placed at the corners:
- Two corners have a positive charge labeled \(+q\).
- One corner has a negative charge labeled \(-q\).
**Solution Explanation:**
To find the point inside the triangle where the electric potential is zero, consider the following:
1. **Electric Potential Due to Point Charges:**
- The electric potential \(V\) at a point due to a charge \(q\) is given by \(V = \frac{kq}{r}\), where \(k\) is Coulomb's constant and \(r\) is the distance from the charge to the point.
2. **Total Electric Potential:**
- Since potential is a scalar quantity, the potentials due to each charge can be added algebraically.
- The total potential \(V_{\text{total}}\) at a point inside the triangle is the sum of the potentials due to the three point charges.
3. **Zero Potential Condition:**
- For the potential to be zero, the sum of potentials due to all charges must equal zero:
\[
\frac{k(+q)}{r_1} + \frac{k(+q)}{r_2} + \frac{k(-q)}{r_3} = 0
\]
- Simplifying gives:
\[
\frac{1}{r_1} + \frac{1}{r_2} = \frac{1}{r_3}
\]
4. **Equilateral Triangle:**
- Symmetrically, the point with zero potential will be along the line connecting the negative charge and the center of the triangle, because this configuration allows balancing the contributions.
5. **Using Symmetry:**
- Due to symmetry in an equilateral triangle and the charge placement, this balancing point lies along the perpendicular bisector of the line segment joining the two positive charges and is closer to the negative charge.
Thus, solving the geometric and algebraic symmetry conditions will allow you to find the exact point inside the triangle.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3c39d812-58a1-4630-9d2c-3fab5b52adb8%2Fdc401439-42bc-4c12-9f09-3d68d656b179%2Fylyvm85_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem:**
Find a point INSIDE the triangle where the electric POTENTIAL is zero when 3 point charges occupy the 3 corners of an equilateral triangle as illustrated? Please explain.
**Diagram Explanation:**
- The triangle is equilateral, meaning all sides have equal length.
- There are three point charges placed at the corners:
- Two corners have a positive charge labeled \(+q\).
- One corner has a negative charge labeled \(-q\).
**Solution Explanation:**
To find the point inside the triangle where the electric potential is zero, consider the following:
1. **Electric Potential Due to Point Charges:**
- The electric potential \(V\) at a point due to a charge \(q\) is given by \(V = \frac{kq}{r}\), where \(k\) is Coulomb's constant and \(r\) is the distance from the charge to the point.
2. **Total Electric Potential:**
- Since potential is a scalar quantity, the potentials due to each charge can be added algebraically.
- The total potential \(V_{\text{total}}\) at a point inside the triangle is the sum of the potentials due to the three point charges.
3. **Zero Potential Condition:**
- For the potential to be zero, the sum of potentials due to all charges must equal zero:
\[
\frac{k(+q)}{r_1} + \frac{k(+q)}{r_2} + \frac{k(-q)}{r_3} = 0
\]
- Simplifying gives:
\[
\frac{1}{r_1} + \frac{1}{r_2} = \frac{1}{r_3}
\]
4. **Equilateral Triangle:**
- Symmetrically, the point with zero potential will be along the line connecting the negative charge and the center of the triangle, because this configuration allows balancing the contributions.
5. **Using Symmetry:**
- Due to symmetry in an equilateral triangle and the charge placement, this balancing point lies along the perpendicular bisector of the line segment joining the two positive charges and is closer to the negative charge.
Thus, solving the geometric and algebraic symmetry conditions will allow you to find the exact point inside the triangle.
Expert Solution
Step 1
Potential due to a charge at a point which is at a distance r from the the charge is given as
V = kq/r
Let the point is at a distance r1 from positive charges and at distance r2 from negative charge.
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
