The Question is from neet-physics electrostatic-charges-and-fields , and it was created by the author ABDUL JILANI BASHA

Question

Two point charges $+q$ and $-q$ are placed at a distance $d$ apart. The locus of points where the electric potential is zero is a:

ABDUL JILANI BASHA · Accepted Answer

## CORE INFORMATION
✓ **Answer**: B
## CONCEPT FRAMEWORK
 **Primary Concept**: Electric potential due to point charges
 **Related Topics**: Electrostatics, equipotential surfaces
 **Prerequisites**: Understanding of electric potential, superposition principle
## SOLUTION PATHWAY
**Given Information**:
  Two point charges: $+q$ and $-q$
  Distance between charges: $d$
  Electric potential = 0
**Method & Steps**:
 1. Determine the expression for electric potential due to a point charge.
  Reasoning: The electric potential $V$ at a distance $r$ from a point charge $Q$ is given by $V = k\frac{Q}{r}$, where $k$ is Coulomb's constant.
  Formula/Rule: $V = k\frac{Q}{r}$
 2. Apply the superposition principle to find the total potential at a point P due to both charges.
  Working: Let P be a point at a distance $r_1$ from $+q$ and $r_2$ from $-q$. The total potential at P is $V_P = k\frac{q}{r_1} - k\frac{q}{r_2}$.  We are looking for points where $V_P = 0$.
  Key Point: The superposition principle states that the total potential at a point due to multiple charges is the algebraic sum of the potentials due to each individual charge.
 3. Solve for the locus of points where $V_P = 0$.
  Result: Setting $V_P = 0$, we get $k\frac{q}{r_1} - k\frac{q}{r_2} = 0$, which simplifies to $r_1 = r_2$. This means the point P is equidistant from both charges. The locus of points equidistant from two points is a plane perpendicular to the line joining the two points and passing through the midpoint.
  Verification: Any point on this plane will be equidistant from both charges, resulting in zero potential.
 ## OPTION ANALYSIS
A :x: A sphere centered at the midpoint would include points closer to one charge than the other, resulting in non-zero potential.
B ✓: A plane perpendicular to the line joining the charges and passing through the midpoint ensures equal distances from both charges, leading to zero potential.
C :x: A sphere centered at the positive charge would have points closer to the positive charge, resulting in a positive potential.
D :x: A sphere centered at the negative charge would have points closer to the negative charge, resulting in a negative potential.
 ## LEARNING AIDS
 **Common Mistakes**:
  1.Incorrectly applying the superposition principle (e.g., adding magnitudes instead of considering signs).
   How to avoid: Remember that potential is a scalar quantity; use the correct signs of the charges when summing.
  2.Confusing electric potential with electric field.
   How to avoid: Understand the difference between these two concepts. Electric field is a vector, while potential is a scalar.
 **Quick Tips**:
  1.Visualize the problem: Sketch the charges and think about the points where the potential due to each charge will cancel out.
  2.Remember that the potential is zero on the perpendicular bisector of the line joining two equal and opposite charges.

ABDUL JILANI BASHA · Answer

Sphere centered at the midpoint of the line joining the charges.

ABDUL JILANI BASHA · Answer

The correct Option is "Plane perpendicular to the line joining the charges and passing through the midpoint."

ABDUL JILANI BASHA · Answer

Sphere centered at the positive charge.

ABDUL JILANI BASHA · Answer

Sphere centered at the negative charge.

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