Why can the net force on a third charge not be zero between +1.07 μC and −3.28 μC?

Both forces point the same way, so they add

The forces are equal in size but cancel only at the midpoint

Opposite charges screen each other's field

The forces are perpendicular there

Outside the charges, on which side does the net force vanish?

Beside the smaller-magnitude charge q1

At the midpoint outside the line

Where is the third charge placed, and does it depend on its own charge?

82.3 cm from q1 away from q2; independent of its sign and size

30.9 cm from q1 between the charges; depends on its sign

82.3 cm from q2 beyond q1; depends on its magnitude

61.8 cm from q1; independent of its sign

2071 Chaitra · 5 marks

Position of third charge for zero force

Short answer

Place the third charge on the line outside the two charges, near the smaller magnitude (+1.07 μC). Balance condition: 1.07/x² = 3.28/(x+61.8)² gives x ≈ 82.3 cm from +1.07 μC, 144.1 cm from −3.28 μC.

Two fixed charges 1.07 μC and −3.28 μC are 61.8 cm apart, where may a third charge be located so that no net force acts on it?

Given q₁ = +1.07 μC, q₂ = −3.28 μC, separation d = 61.8 cm.

Where can the net force be zero?

Between the charges: the forces on a third charge from opposite charges point in the same direction, so they cannot cancel.
Outside the charges: the forces are opposite in direction. They can balance only on the side of the smaller-magnitude charge (q₁): there the third charge is closer to the weaker charge, so the shorter distance makes up for its smaller size.

  third charge     q1 (+1.07)          q2 (-3.28)
       o---------------(+)----------------(-)
       <------ x ------><-------- d -------->

Let the third charge be at distance x from q₁, on the side away from q₂. Its distance from q₂ is (x + d).

Condition

|q₁| / x² = |q₂| / (x + d)²

(x + d)/x = √(|q₂|/|q₁|) = √(3.28/1.07) = √3.065 = 1.751

1 + d/x = 1.751 → d/x = 0.751 → x = 61.8 / 0.751 = 82.3 cm

Check: 1.07/(0.823)² = 1.58 and 3.28/(1.441)² = 1.58 (μC/m²). ✓

Answer: the third charge should be placed on the line joining the charges, outside them, 82.3 cm from the +1.07 μC charge on the side away from the −3.28 μC charge (144.1 cm from the −3.28 μC charge). The result is independent of the third charge's sign and magnitude.

✓ Answer checked by Claude Opus 5.5 (high effort)

Zero potential between two charges · Engineering Physics, chapter 7
SHM of charge between two positive charges · Engineering Physics, chapter 7 · asked 3×
Third bright fringe separation, two wavelengths · Engineering Physics, chapter 4
Image by two lenses 30 cm and 40 cm · Engineering Physics, chapter 5 · asked 3×
Position of 2t force for zero net elongation · Strength of Materials, chapter 3
Point charge and four line charges, D · Electromagnetism, chapter 2
NO₂ and SO₂ sources; role in acid rain · Engineering Chemistry, chapter 3
Flux through sphere, two line charges · Electromagnetism, chapter 2

All Engineering Physics chapter 7 questions →

Position of third charge for zero force

Where can the net force be zero?

Condition

Related questions