Q41. Three charges q, -q, q placed at the vertices of an equilateral triangle as shown in figure. Wh

Q: What is the correct answer for CUET UG Physics Q41?

The correct answer is c. There is a significant inconsistency in the question: the text describes charges `q, -q, q` at vertices of an equilateral triangle, while the diagram shows charges `2q, q, q`. Also, the options in the paper contain `l` instead of `l²` in the denominator, which is dimensionally incorrect for force. Assuming the diagram is correct, with charges `2q` at vertex 1 (top), `q` at vertex 2 (bottom-left),

Q: Q41. Three charges q, -q, q placed at the vertices of an equilateral triangle as shown in figure. What is the magnitude of force on charge placed at position 3 due to the presence of other two…

The correct answer is c. There is a significant inconsistency in the question: the text describes charges `q, -q, q` at vertices of an equilateral triangle, while the diagram shows charges `2q, q, q`. Also, the options in the paper contain `l` instead of `l²` in the denominator, which is dimensionally incorrect for force. Assuming the diagram is correct, with charges `2q` at vertex 1 (top), `q` at vertex 2 (bottom-left),

Q: What are the options for this CUET UG Physics question?

A. 1q²/(2πε₀l²) · B. √3q²/(4πε₀l²) · C. √5q²/(8πε₀l²) · D. 1q²/(4πε₀l²)

Question

Q41. Three charges q, -q, q placed at the vertices of an equilateral triangle as shown in figure. What is the magnitude of force on charge placed at position 3 due to the presence of other two charges?
(a) 1q²/(2πε₀l²)
(b) √3q²/(4πε₀l²)
(c) √5q²/(8πε₀l²)
(d) 1q²/(4πε₀l²)

FirstInTest · Accepted Answer

There is a significant inconsistency in the question: the text describes charges `q, -q, q` at vertices of an equilateral triangle, while the diagram shows charges `2q, q, q`. Also, the options in the paper contain `l` instead of `l²` in the denominator, which is dimensionally incorrect for force. Assuming the diagram is correct, with charges `2q` at vertex 1 (top), `q` at vertex 2 (bottom-left), and `q` at vertex 3 (bottom-right), and side length `l` for an equilateral triangle.We calculate the force on `q` at vertex 3:1.  Force `F₁₃` on `q` (at 3) due to `2q` (at 1): It's repulsive. Magnitude `F₁₃ = (1/4πε₀) * (2q * q) / l² = 2kq²/l²`, where `k = 1/(4πε₀)`. Let `kq²/l² = F₀`. So `F₁₃ = 2F₀`.2.  Force `F₂₃` on `q` (at 3) due to `q` (at 2): It's repulsive. Magnitude `F₂₃ = (1/4πε₀) * (q * q) / l² = kq²/l² = F₀`.Let's use coordinate system with vertex 3 at `(0,0)`, vertex 2 at `(l,0)`. Vertex 1 will be at `(l/2, l√3/2)`.Vector from 3 to 2 is `(l,0)`, so `F₂₃` (repulsive from q at 2 on q at 3) is along `-x` direction. `F₂₃ = -F₀ î`.Vector from 3 to 1 is `(l/2, l√3/2)`. So `F₁₃` (repulsive from 2q at 1 on q at 3) is along the vector from 1 to 3, which is `(-l/2, -l√3/2)`. Unit vector `(-1/2 î - √3/2 ĵ)`.`F₁₃ = (2F₀) * (-1/2 î - √3/2 ĵ) = -F₀ î - √3F₀ ĵ`.Net force `F_net = F₁₃ + F₂₃ = (-F₀ î - √3F₀ ĵ) + (-F₀ î) = -2F₀ î - √3F₀ ĵ`.Magnitude `|F_net| = √( (-2F₀)² + (-√3F₀)² ) = √(4F₀² + 3F₀²) = √(7F₀²) = √7 F₀`.Substituting `F₀ = q²/(4πε₀l²)`, we get `|F_net| = √7 q²/(4πε₀l²)`. This is not among the options. If we assume the general case of `q, -q, q` at vertices, the resultant force is `q²/(4πε₀l²)`. Given the answer is (c) `√5q²/(8πε₀l²)`, it suggests a different setup or interpretation not immediately evident from the provided image or text. Without further clarification, standard calculations do not yield this option.

Answer

1q²/(2πε₀l²)

Answer

√3q²/(4πε₀l²)

Answer

√5q²/(8πε₀l²)

Answer

1q²/(4πε₀l²)

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