The Question is from neet-physics electrostatics electric-potential-and-potential-energy, and it was created by the author VENKATESWARARAO

Question

Two point charges +q and -2q are placed a distance 'd' apart. At what distance along the line joining the two charges is the electric potential zero?

VENKATESWARARAO · Accepted Answer

## CORE INFORMATION
✓ **Answer**: A
## CONCEPT FRAMEWORK
 **Primary Concept**: Electric Potential due to point charges
 **Related Topics**: Electrostatics, Coulomb's Law
 **Prerequisites**: Understanding of electric potential, superposition principle.
## SOLUTION PATHWAY
**Given Information**:
  Two point charges: +q and -2q
  Distance between charges: d
  Electric potential at a point: V = 0
**Method & Steps**:
 1. Let the point where the electric potential is zero be at a distance x from the charge +q along the line joining the two charges.
  Reasoning: The electric potential due to a point charge is given by $V = k\frac{Q}{r}$, where k is Coulomb's constant, Q is the charge, and r is the distance from the charge.
  Formula/Rule: $V = k\frac{q}{x} + k\frac{-2q}{d-x} = 0$
 2. Solve the equation for x:
  Working: $\frac{q}{x} = \frac{2q}{d-x}$
  $\frac{1}{x} = \frac{2}{d-x}$
  $d-x = 2x$
  $3x = d$
  $x = \frac{d}{3}$
  Key Point: The potential is zero at a point closer to the smaller charge (+q) because it has a smaller magnitude. 
 3. The point where the potential is zero is at a distance d/3 from +q towards -2q.
  Result: d/3 from +q towards -2q
  Verification: Substitute x = d/3 back into the potential equation to confirm it equals zero.
 ## OPTION ANALYSIS
A ✓: d/3 from +q towards -2q: This is the correct solution, as derived above.
B :x: d/3 from -2q towards +q: This would place the zero-potential point closer to the larger charge, which is incorrect.
C :x: 2d/3 from +q towards -2q: This places the zero-potential point too far from the smaller charge.
D :x: 2d/3 from -2q towards +q: This places the zero-potential point too far from the smaller charge.
 ## LEARNING AIDS
 **Common Mistakes**:
  1.Incorrectly applying the superposition principle: Remember to consider the signs of the charges when summing the potentials.
  2.Algebraic errors when solving for x: Double-check your calculations to ensure accuracy.
 **Quick Tips**:
  1.Remember that the zero-potential point will always be closer to the smaller charge in magnitude.
  2.Visualize the problem: Drawing a diagram can help understand the relative positions of the charges and the zero-potential point.

VENKATESWARARAO · Answer

The correct Option is "d/3 from +q towards -2q"

VENKATESWARARAO · Answer

d/3 from -2q towards +q

VENKATESWARARAO · Answer

2d/3 from +q towards -2q

VENKATESWARARAO · Answer

2d/3 from -2q towards +q

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